# 高階導數基礎 · 脈衝 R02

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261014-advance-20261111-r02-higher-order-derivative-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[1,2,3,4],"order":0}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 0, 是, f_zero_equals_f, 是)

Wave6第五層核對=(3, 0, 是, f_zero_equals_f, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0001/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 2. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[2,4,6,8,10],"order":1}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 1, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 1, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0002/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 3. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[3,6,9,12,15,18],"order":2}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 2, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(5, 2, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0003/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 4. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[4,8,12,16,20,24,28],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0004/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 5. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[5,10,15,20],"order":4}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 4, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(3, 4, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0005/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 6. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[6,12,18,24,30],"order":5}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 5, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 5, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0006/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 7. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[7,14,21,28,35,42],"order":6}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 6, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(5, 6, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0007/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 8. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[8,16,24,32,40,48,56],"order":7}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 7, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 7, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0008/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 9. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[9,18,27,36],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(3, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0009/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 10. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[10,20,30,40,50],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0010/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 11. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[11,22,33,44,55,66],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(5, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0011/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 12. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[12,24,36,48,60,72,84],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0012/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 13. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[13,26,39,52],"order":2}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 2, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(3, 2, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0013/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 14. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[14,28,42,56,70],"order":1}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 1, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 1, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0014/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 15. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[15,30,45,60,75,90],"order":0}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 0, 是, f_zero_equals_f, 是)

Wave6第五層核對=(5, 0, 是, f_zero_equals_f, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0015/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 16. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[16,32,48,64,80,96,112],"order":7}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 7, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 7, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0016/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 17. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[17,34,51,68],"order":1}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 1, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(3, 1, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0017/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 18. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[18,36,54,72,90],"order":5}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 5, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 5, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0018/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 19. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[19,38,57,76,95,114],"order":4}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 4, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(5, 4, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0019/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 20. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[20,40,60,80,100,120,140],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0020/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 21. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[21,42,63,84],"order":0}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 0, 是, f_zero_equals_f, 是)

Wave6第五層核對=(3, 0, 是, f_zero_equals_f, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0021/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 22. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[22,44,66,88,110],"order":3}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(4, 3, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(4, 3, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0022/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 23. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[23,46,69,92,115,138],"order":1}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(5, 1, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(5, 1, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0023/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 24. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[24,48,72,96,120,144,168],"order":7}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(6, 7, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(6, 7, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0024/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 25. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-order-qualification；資料={"coefficients":[25,50,75,100],"order":4}。請依 [declared_degree_bound, order, nonnegative_order, order_convention, polynomial_chain_certificate] 欄序回答。

declared_degree_bound是原coefficient array長度減1；若synthetic輸入有trailing zeros，這是上界，不宣稱為約去零係數後的最小degree。

查看答案與解釋(3, 4, 是, recursive_derivative_chain_required, 是)

Wave6第五層核對=(3, 4, 是, recursive_derivative_chain_required, 是)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0025/)

高階導數 · qf-mod42-higher-order-qualification · candidate





## 26. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[1,2,3,4],"order":0,"point":-2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([1, 2, 3, 4], 0, [1, 2, 3, 4], -2, -23, falling_factorial_coefficients_exact)

Wave6第五層核對=([1, 2, 3, 4], 0, [1, 2, 3, 4], -2, -23, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0026/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 27. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[2,4,6,8,10],"order":1,"point":-1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([2, 4, 6, 8, 10], 1, [4, 12, 24, 40], -1, -24, falling_factorial_coefficients_exact)

Wave6第五層核對=([2, 4, 6, 8, 10], 1, [4, 12, 24, 40], -1, -24, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0027/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 28. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[3,6,9,12,15,18],"order":2,"point":0}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([3, 6, 9, 12, 15, 18], 2, [18, 72, 180, 360], 0, 18, falling_factorial_coefficients_exact)

Wave6第五層核對=([3, 6, 9, 12, 15, 18], 2, [18, 72, 180, 360], 0, 18, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0028/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 29. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[4,8,12,16,20,24,28],"order":3,"point":1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([4, 8, 12, 16, 20, 24, 28], 3, [96, 480, 1440, 3360], 1, 5376, falling_factorial_coefficients_exact)

Wave6第五層核對=([4, 8, 12, 16, 20, 24, 28], 3, [96, 480, 1440, 3360], 1, 5376, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0029/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 30. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[5,10,15,20],"order":4,"point":2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([5, 10, 15, 20], 4, [0], 2, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([5, 10, 15, 20], 4, [0], 2, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0030/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 31. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[6,12,18,24,30],"order":5,"point":-2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([6, 12, 18, 24, 30], 5, [0], -2, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([6, 12, 18, 24, 30], 5, [0], -2, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0031/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 32. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[7,14,21,28,35,42],"order":6,"point":-1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([7, 14, 21, 28, 35, 42], 6, [0], -1, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([7, 14, 21, 28, 35, 42], 6, [0], -1, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0032/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 33. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[8,16,24,32,40,48,56],"order":7,"point":0}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([8, 16, 24, 32, 40, 48, 56], 7, [0], 0, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([8, 16, 24, 32, 40, 48, 56], 7, [0], 0, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0033/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 34. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[9,18,27,36],"order":3,"point":1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([9, 18, 27, 36], 3, [216], 1, 216, falling_factorial_coefficients_exact)

Wave6第五層核對=([9, 18, 27, 36], 3, [216], 1, 216, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0034/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 35. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[10,20,30,40,50],"order":3,"point":2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([10, 20, 30, 40, 50], 3, [240, 1200], 2, 2640, falling_factorial_coefficients_exact)

Wave6第五層核對=([10, 20, 30, 40, 50], 3, [240, 1200], 2, 2640, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0035/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 36. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[11,22,33,44,55,66],"order":3,"point":-2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([11, 22, 33, 44, 55, 66], 3, [264, 1320, 3960], -2, 13464, falling_factorial_coefficients_exact)

Wave6第五層核對=([11, 22, 33, 44, 55, 66], 3, [264, 1320, 3960], -2, 13464, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0036/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 37. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[12,24,36,48,60,72,84],"order":3,"point":-1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([12, 24, 36, 48, 60, 72, 84], 3, [288, 1440, 4320, 10080], -1, -6912, falling_factorial_coefficients_exact)

Wave6第五層核對=([12, 24, 36, 48, 60, 72, 84], 3, [288, 1440, 4320, 10080], -1, -6912, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0037/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 38. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[13,26,39,52],"order":2,"point":0}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([13, 26, 39, 52], 2, [78, 312], 0, 78, falling_factorial_coefficients_exact)

Wave6第五層核對=([13, 26, 39, 52], 2, [78, 312], 0, 78, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0038/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 39. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[14,28,42,56,70],"order":1,"point":1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([14, 28, 42, 56, 70], 1, [28, 84, 168, 280], 1, 560, falling_factorial_coefficients_exact)

Wave6第五層核對=([14, 28, 42, 56, 70], 1, [28, 84, 168, 280], 1, 560, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0039/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 40. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[15,30,45,60,75,90],"order":0,"point":2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([15, 30, 45, 60, 75, 90], 0, [15, 30, 45, 60, 75, 90], 2, 4815, falling_factorial_coefficients_exact)

Wave6第五層核對=([15, 30, 45, 60, 75, 90], 0, [15, 30, 45, 60, 75, 90], 2, 4815, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0040/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 41. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[16,32,48,64,80,96,112],"order":7,"point":-2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([16, 32, 48, 64, 80, 96, 112], 7, [0], -2, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([16, 32, 48, 64, 80, 96, 112], 7, [0], -2, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0041/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 42. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[17,34,51,68],"order":1,"point":-1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([17, 34, 51, 68], 1, [34, 102, 204], -1, 136, falling_factorial_coefficients_exact)

Wave6第五層核對=([17, 34, 51, 68], 1, [34, 102, 204], -1, 136, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0042/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 43. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[18,36,54,72,90],"order":5,"point":0}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([18, 36, 54, 72, 90], 5, [0], 0, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([18, 36, 54, 72, 90], 5, [0], 0, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0043/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 44. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[19,38,57,76,95,114],"order":4,"point":1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([19, 38, 57, 76, 95, 114], 4, [2280, 13680], 1, 15960, falling_factorial_coefficients_exact)

Wave6第五層核對=([19, 38, 57, 76, 95, 114], 4, [2280, 13680], 1, 15960, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0044/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 45. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[20,40,60,80,100,120,140],"order":3,"point":2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([20, 40, 60, 80, 100, 120, 140], 3, [480, 2400, 7200, 16800], 2, 168480, falling_factorial_coefficients_exact)

Wave6第五層核對=([20, 40, 60, 80, 100, 120, 140], 3, [480, 2400, 7200, 16800], 2, 168480, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0045/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 46. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[21,42,63,84],"order":0,"point":-2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([21, 42, 63, 84], 0, [21, 42, 63, 84], -2, -483, falling_factorial_coefficients_exact)

Wave6第五層核對=([21, 42, 63, 84], 0, [21, 42, 63, 84], -2, -483, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0046/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 47. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[22,44,66,88,110],"order":3,"point":-1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([22, 44, 66, 88, 110], 3, [528, 2640], -1, -2112, falling_factorial_coefficients_exact)

Wave6第五層核對=([22, 44, 66, 88, 110], 3, [528, 2640], -1, -2112, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0047/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 48. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[23,46,69,92,115,138],"order":1,"point":0}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([23, 46, 69, 92, 115, 138], 1, [46, 138, 276, 460, 690], 0, 46, falling_factorial_coefficients_exact)

Wave6第五層核對=([23, 46, 69, 92, 115, 138], 1, [46, 138, 276, 460, 690], 0, 46, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0048/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 49. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[24,48,72,96,120,144,168],"order":7,"point":1}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([24, 48, 72, 96, 120, 144, 168], 7, [0], 1, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([24, 48, 72, 96, 120, 144, 168], 7, [0], 1, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0049/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 50. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-polynomial-nth-derivative；資料={"coefficients":[25,50,75,100],"order":4,"point":2}。請依 [coefficients, order, derivative_coefficients, point, value, certificate] 欄序回答。

查看答案與解釋([25, 50, 75, 100], 4, [0], 2, 0, falling_factorial_coefficients_exact)

Wave6第五層核對=([25, 50, 75, 100], 4, [0], 2, 0, falling_factorial_coefficients_exact)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0050/)

高階導數 · qf-mod42-higher-polynomial-nth-derivative · candidate





## 51. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[1,2,3,4],"order":4,"point":-2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 4, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 4, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0051/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 52. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[2,4,6,8,10],"order":6,"point":-1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 6, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 6, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0052/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 53. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[3,6,9,12,15,18],"order":8,"point":0}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 8, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 8, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0053/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 54. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[4,8,12,16,20,24,28],"order":7,"point":1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 7, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 7, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0054/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 55. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[5,10,15,20],"order":5,"point":2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 5, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 5, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0055/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 56. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[6,12,18,24,30],"order":7,"point":-2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0056/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 57. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[7,14,21,28,35,42],"order":6,"point":-1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 6, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 6, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0057/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 58. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[8,16,24,32,40,48,56],"order":8,"point":0}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 8, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 8, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0058/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 59. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[9,18,27,36],"order":6,"point":1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0059/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 60. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[10,20,30,40,50],"order":5,"point":2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 5, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 5, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0060/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 61. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[11,22,33,44,55,66],"order":7,"point":-2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0061/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 62. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[12,24,36,48,60,72,84],"order":9,"point":-1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 9, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 9, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0062/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 63. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[13,26,39,52],"order":4,"point":0}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 4, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 4, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0063/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 64. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[14,28,42,56,70],"order":6,"point":1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0064/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 65. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[15,30,45,60,75,90],"order":8,"point":2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 8, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 8, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0065/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 66. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[16,32,48,64,80,96,112],"order":7,"point":-2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 7, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0066/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 67. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[17,34,51,68],"order":5,"point":-1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 5, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 5, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0067/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 68. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[18,36,54,72,90],"order":7,"point":0}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 7, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 7, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0068/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 69. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[19,38,57,76,95,114],"order":6,"point":1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 6, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0069/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 70. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[20,40,60,80,100,120,140],"order":8,"point":2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 8, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 8, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0070/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 71. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[21,42,63,84],"order":6,"point":-2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 6, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 6, [0], -2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0071/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 72. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[22,44,66,88,110],"order":5,"point":-1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(4, 5, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(4, 5, [0], -1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0072/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 73. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[23,46,69,92,115,138],"order":7,"point":0}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(5, 7, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(5, 7, [0], 0, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0073/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 74. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[24,48,72,96,120,144,168],"order":9,"point":1}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(6, 9, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(6, 9, [0], 1, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0074/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 75. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-zero-beyond-degree；資料={"coefficients":[25,50,75,100],"order":4,"point":2}。請依 [declared_degree_bound, order, derivative_coefficients, point, value, zero_derivative_certificate, certificate] 欄序回答。

查看答案與解釋(3, 4, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)

Wave6第五層核對=(3, 4, [0], 2, 0, 是, orders_above_polynomial_degree_are_zero_without_analyticity_claim)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0075/)

高階導數 · qf-mod42-higher-zero-beyond-degree · candidate





## 76. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":1}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(1, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(1, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0076/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 77. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":2}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(2, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(2, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0077/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 78. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":3}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(3, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(3, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0078/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 79. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":4}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(4, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(4, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0079/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 80. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":5}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(5, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(5, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0080/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 81. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":6}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(6, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(6, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0081/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 82. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":7}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(7, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(7, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0082/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 83. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":8}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(8, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(8, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0083/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 84. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":9}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(9, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(9, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0084/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 85. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":10}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(10, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(10, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0085/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 86. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":11}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(11, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(11, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0086/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 87. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":12}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(12, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(12, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0087/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 88. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":13}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(13, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(13, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0088/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 89. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":14}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(14, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(14, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0089/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 90. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":15}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(15, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(15, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0090/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 91. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":16}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(16, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(16, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0091/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 92. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":17}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(17, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(17, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0092/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 93. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":18}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(18, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(18, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0093/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 94. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":19}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(19, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(19, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0094/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 95. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":20}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(20, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(20, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0095/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 96. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":21}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(21, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(21, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0096/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 97. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":22}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(22, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(22, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0097/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 98. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":23}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(23, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(23, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0098/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 99. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":24}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(24, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(24, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0099/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate





## 100. 高階導數

f^(0)=f且f^(n+1)=(f^n)'的逐階存在與n in natural including zero。操作=higher-missing-next-order-boundary；資料={"scale":25}。請依 [scale, function_description, point, first_derivative_exists, first_derivative_value, second_derivative_exists, boundary] 欄序回答。

查看答案與解釋(25, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)

Wave6第五層核對=(25, f(x)=scale*x*abs(x), 0, 是, 0, 否, first_derivative_exists_at_zero_but_second_derivative_has_opposite_one_sided_limits)；依完整明示資料獨立重算；polynomial nth derivative使用falling-factorial coefficients且order超過degree後為zero；存在第n階不推出第n+1階，也不推出analytic或Taylor series convergence。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261111-r02-higher-order-derivative-0100/)

高階導數 · qf-mod42-higher-missing-next-order-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r02-higher-order-derivative-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261111-r02-higher-order-derivative-foundations/validation-report.json)