# 微分中值定理基礎 · 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-20261110-r02-mean-value-theorem-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. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":1,"B":-10,"C":1,"a":-2,"b":3}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

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

Wave6第四層核對=(-2, 3, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0001/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 2. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":2,"B":-9,"C":2,"a":-3,"b":4}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

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

Wave6第四層核對=(-3, 4, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0002/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 3. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":3,"B":-8,"C":5,"a":-4,"b":5}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

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

Wave6第四層核對=(-4, 5, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0003/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 4. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":4,"B":-7,"C":10,"a":-5,"b":6}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

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

Wave6第四層核對=(-5, 6, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0004/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 5. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":5,"B":-6,"C":17,"a":-6,"b":7}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

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

Wave6第四層核對=(-6, 7, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0005/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 6. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":1,"B":-5,"C":26,"a":-7,"b":8}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-7, 8, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-7, 8, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0006/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 7. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":2,"B":-4,"C":37,"a":-8,"b":9}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-8, 9, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-8, 9, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0007/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 8. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":3,"B":-3,"C":50,"a":-9,"b":10}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-9, 10, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-9, 10, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0008/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 9. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":4,"B":-2,"C":65,"a":-10,"b":11}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-10, 11, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-10, 11, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0009/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 10. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":5,"B":-1,"C":82,"a":-11,"b":12}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-11, 12, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-11, 12, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0010/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 11. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":1,"B":0,"C":101,"a":-12,"b":13}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-12, 13, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-12, 13, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0011/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 12. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":2,"B":1,"C":122,"a":-13,"b":14}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-13, 14, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-13, 14, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0012/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 13. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":3,"B":2,"C":145,"a":-14,"b":15}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-14, 15, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-14, 15, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0013/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 14. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":4,"B":3,"C":170,"a":-15,"b":16}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-15, 16, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-15, 16, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0014/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 15. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":5,"B":4,"C":197,"a":-16,"b":17}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-16, 17, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-16, 17, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0015/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 16. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":1,"B":5,"C":226,"a":-17,"b":18}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-17, 18, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-17, 18, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0016/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 17. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":2,"B":6,"C":257,"a":-18,"b":19}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-18, 19, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-18, 19, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0017/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 18. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":3,"B":7,"C":290,"a":-19,"b":20}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-19, 20, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-19, 20, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0018/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 19. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":4,"B":8,"C":325,"a":-20,"b":21}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-20, 21, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-20, 21, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0019/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 20. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":5,"B":9,"C":362,"a":-21,"b":22}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-21, 22, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-21, 22, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0020/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 21. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":1,"B":10,"C":401,"a":-22,"b":23}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-22, 23, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-22, 23, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0021/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 22. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":2,"B":11,"C":442,"a":-23,"b":24}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-23, 24, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-23, 24, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0022/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 23. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":3,"B":12,"C":485,"a":-24,"b":25}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-24, 25, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-24, 25, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0023/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 24. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":4,"B":13,"C":530,"a":-25,"b":26}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-25, 26, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-25, 26, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0024/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 25. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-hypothesis-audit；資料={"A":5,"B":14,"C":577,"a":-26,"b":27}。請依 [a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate] 欄序回答。

查看答案與解釋(-26, 27, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

Wave6第四層核對=(-26, 27, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0025/)

微分中值定理 · qf-mod41-mvt-hypothesis-audit · candidate





## 26. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":1,"B":-10,"C":1,"a":-2,"b":3}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(25, -20, 5, -9, exact_endpoint_secant_slope)

Wave6第四層核對=(25, -20, 5, -9, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0026/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 27. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":2,"B":-9,"C":2,"a":-3,"b":4}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(47, -2, 7, -7, exact_endpoint_secant_slope)

Wave6第四層核對=(47, -2, 7, -7, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0027/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 28. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":3,"B":-8,"C":5,"a":-4,"b":5}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(85, 40, 9, -5, exact_endpoint_secant_slope)

Wave6第四層核對=(85, 40, 9, -5, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0028/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 29. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":4,"B":-7,"C":10,"a":-5,"b":6}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(145, 112, 11, -3, exact_endpoint_secant_slope)

Wave6第四層核對=(145, 112, 11, -3, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0029/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 30. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":5,"B":-6,"C":17,"a":-6,"b":7}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(233, 220, 13, -1, exact_endpoint_secant_slope)

Wave6第四層核對=(233, 220, 13, -1, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0030/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 31. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":1,"B":-5,"C":26,"a":-7,"b":8}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(110, 50, 15, -4, exact_endpoint_secant_slope)

Wave6第四層核對=(110, 50, 15, -4, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0031/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 32. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":2,"B":-4,"C":37,"a":-8,"b":9}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(197, 163, 17, -2, exact_endpoint_secant_slope)

Wave6第四層核對=(197, 163, 17, -2, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0032/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 33. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":3,"B":-3,"C":50,"a":-9,"b":10}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(320, 320, 19, 0, exact_endpoint_secant_slope)

Wave6第四層核對=(320, 320, 19, 0, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0033/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 34. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":4,"B":-2,"C":65,"a":-10,"b":11}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(485, 527, 21, 2, exact_endpoint_secant_slope)

Wave6第四層核對=(485, 527, 21, 2, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0034/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 35. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":5,"B":-1,"C":82,"a":-11,"b":12}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(698, 790, 23, 4, exact_endpoint_secant_slope)

Wave6第四層核對=(698, 790, 23, 4, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0035/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 36. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":1,"B":0,"C":101,"a":-12,"b":13}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(245, 270, 25, 1, exact_endpoint_secant_slope)

Wave6第四層核對=(245, 270, 25, 1, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0036/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 37. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":2,"B":1,"C":122,"a":-13,"b":14}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(447, 528, 27, 3, exact_endpoint_secant_slope)

Wave6第四層核對=(447, 528, 27, 3, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0037/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 38. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":3,"B":2,"C":145,"a":-14,"b":15}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(705, 850, 29, 5, exact_endpoint_secant_slope)

Wave6第四層核對=(705, 850, 29, 5, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0038/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 39. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":4,"B":3,"C":170,"a":-15,"b":16}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1025, 1242, 31, 7, exact_endpoint_secant_slope)

Wave6第四層核對=(1025, 1242, 31, 7, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0039/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 40. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":5,"B":4,"C":197,"a":-16,"b":17}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1413, 1710, 33, 9, exact_endpoint_secant_slope)

Wave6第四層核對=(1413, 1710, 33, 9, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0040/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 41. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":1,"B":5,"C":226,"a":-17,"b":18}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(430, 640, 35, 6, exact_endpoint_secant_slope)

Wave6第四層核對=(430, 640, 35, 6, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0041/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 42. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":2,"B":6,"C":257,"a":-18,"b":19}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(797, 1093, 37, 8, exact_endpoint_secant_slope)

Wave6第四層核對=(797, 1093, 37, 8, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0042/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 43. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":3,"B":7,"C":290,"a":-19,"b":20}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1240, 1630, 39, 10, exact_endpoint_secant_slope)

Wave6第四層核對=(1240, 1630, 39, 10, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0043/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 44. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":4,"B":8,"C":325,"a":-20,"b":21}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1765, 2257, 41, 12, exact_endpoint_secant_slope)

Wave6第四層核對=(1765, 2257, 41, 12, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0044/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 45. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":5,"B":9,"C":362,"a":-21,"b":22}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(2378, 2980, 43, 14, exact_endpoint_secant_slope)

Wave6第四層核對=(2378, 2980, 43, 14, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0045/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 46. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":1,"B":10,"C":401,"a":-22,"b":23}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(665, 1160, 45, 11, exact_endpoint_secant_slope)

Wave6第四層核對=(665, 1160, 45, 11, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0046/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 47. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":2,"B":11,"C":442,"a":-23,"b":24}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1247, 1858, 47, 13, exact_endpoint_secant_slope)

Wave6第四層核對=(1247, 1858, 47, 13, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0047/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 48. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":3,"B":12,"C":485,"a":-24,"b":25}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(1925, 2660, 49, 15, exact_endpoint_secant_slope)

Wave6第四層核對=(1925, 2660, 49, 15, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0048/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 49. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":4,"B":13,"C":530,"a":-25,"b":26}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(2705, 3572, 51, 17, exact_endpoint_secant_slope)

Wave6第四層核對=(2705, 3572, 51, 17, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0049/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 50. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-secant-slope；資料={"A":5,"B":14,"C":577,"a":-26,"b":27}。請依 [value_at_a, value_at_b, interval_length, secant_slope, certificate] 欄序回答。

查看答案與解釋(3593, 4600, 53, 19, exact_endpoint_secant_slope)

Wave6第四層核對=(3593, 4600, 53, 19, exact_endpoint_secant_slope)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0050/)

微分中值定理 · qf-mod41-mvt-secant-slope · candidate





## 51. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":1,"B":-10,"C":1,"a":-2,"b":3}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -9, -9, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -9, -9, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0051/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 52. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":2,"B":-9,"C":2,"a":-3,"b":4}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -7, -7, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -7, -7, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0052/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 53. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":3,"B":-8,"C":5,"a":-4,"b":5}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -5, -5, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -5, -5, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0053/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 54. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":4,"B":-7,"C":10,"a":-5,"b":6}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -3, -3, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -3, -3, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0054/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 55. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":5,"B":-6,"C":17,"a":-6,"b":7}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -1, -1, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -1, -1, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0055/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 56. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":1,"B":-5,"C":26,"a":-7,"b":8}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -4, -4, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -4, -4, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0056/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 57. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":2,"B":-4,"C":37,"a":-8,"b":9}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, -2, -2, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, -2, -2, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0057/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 58. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":3,"B":-3,"C":50,"a":-9,"b":10}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 0, 0, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 0, 0, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0058/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 59. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":4,"B":-2,"C":65,"a":-10,"b":11}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 2, 2, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 2, 2, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0059/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 60. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":5,"B":-1,"C":82,"a":-11,"b":12}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 4, 4, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 4, 4, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0060/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 61. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":1,"B":0,"C":101,"a":-12,"b":13}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 1, 1, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 1, 1, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0061/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 62. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":2,"B":1,"C":122,"a":-13,"b":14}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 3, 3, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 3, 3, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0062/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 63. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":3,"B":2,"C":145,"a":-14,"b":15}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 5, 5, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 5, 5, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0063/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 64. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":4,"B":3,"C":170,"a":-15,"b":16}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 7, 7, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 7, 7, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0064/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 65. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":5,"B":4,"C":197,"a":-16,"b":17}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 9, 9, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 9, 9, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0065/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 66. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":1,"B":5,"C":226,"a":-17,"b":18}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 6, 6, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 6, 6, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0066/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 67. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":2,"B":6,"C":257,"a":-18,"b":19}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 8, 8, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 8, 8, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0067/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 68. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":3,"B":7,"C":290,"a":-19,"b":20}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 10, 10, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 10, 10, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0068/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 69. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":4,"B":8,"C":325,"a":-20,"b":21}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 12, 12, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 12, 12, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0069/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 70. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":5,"B":9,"C":362,"a":-21,"b":22}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 14, 14, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 14, 14, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0070/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 71. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":1,"B":10,"C":401,"a":-22,"b":23}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 11, 11, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 11, 11, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0071/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 72. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":2,"B":11,"C":442,"a":-23,"b":24}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 13, 13, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 13, 13, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0072/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 73. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":3,"B":12,"C":485,"a":-24,"b":25}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 15, 15, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 15, 15, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0073/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 74. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":4,"B":13,"C":530,"a":-25,"b":26}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 17, 17, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 17, 17, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0074/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 75. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-polynomial-witness；資料={"A":5,"B":14,"C":577,"a":-26,"b":27}。請依 [c, strictly_interior, derivative_at_c, secant_slope, equal, certificate] 欄序回答。

查看答案與解釋(1/2, 是, 19, 19, 是, quadratic_midpoint_witness)

Wave6第四層核對=(1/2, 是, 19, 19, 是, quadratic_midpoint_witness)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0075/)

微分中值定理 · qf-mod41-mvt-polynomial-witness · candidate





## 76. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":0,"b":0,"scale":1,"offset":0}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 0, 0, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 0, 0, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0076/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 77. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-2,"b":3,"scale":2,"offset":1}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -2, 3, 2, 1, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -2, 3, 2, 1, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0077/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 78. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-3,"b":4,"scale":3,"offset":2}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -3, 4, 3, 2, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -3, 4, 3, 2, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0078/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 79. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":3,"b":3,"scale":4,"offset":-3}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 3, 3, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 3, 3, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0079/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 80. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-5,"b":6,"scale":5,"offset":4}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -5, 6, 5, 4, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -5, 6, 5, 4, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0080/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 81. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-6,"b":7,"scale":6,"offset":5}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -6, 7, 6, 5, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -6, 7, 6, 5, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0081/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 82. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":6,"b":6,"scale":7,"offset":-6}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 6, 6, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 6, 6, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0082/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 83. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-8,"b":9,"scale":8,"offset":7}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -8, 9, 8, 7, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -8, 9, 8, 7, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0083/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 84. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-9,"b":10,"scale":9,"offset":8}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -9, 10, 9, 8, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -9, 10, 9, 8, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0084/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 85. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":9,"b":9,"scale":10,"offset":-9}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 9, 9, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 9, 9, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0085/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 86. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-11,"b":12,"scale":11,"offset":10}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -11, 12, 11, 10, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -11, 12, 11, 10, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0086/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 87. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-12,"b":13,"scale":12,"offset":11}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -12, 13, 12, 11, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -12, 13, 12, 11, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0087/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 88. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":12,"b":12,"scale":13,"offset":-12}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 12, 12, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 12, 12, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0088/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 89. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-14,"b":15,"scale":14,"offset":13}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -14, 15, 14, 13, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -14, 15, 14, 13, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0089/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 90. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-15,"b":16,"scale":15,"offset":14}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -15, 16, 15, 14, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -15, 16, 15, 14, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0090/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 91. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":15,"b":15,"scale":16,"offset":-15}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 15, 15, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 15, 15, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0091/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 92. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-17,"b":18,"scale":17,"offset":16}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -17, 18, 17, 16, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -17, 18, 17, 16, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0092/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 93. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-18,"b":19,"scale":18,"offset":17}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -18, 19, 18, 17, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -18, 19, 18, 17, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0093/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 94. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":18,"b":18,"scale":19,"offset":-18}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 18, 18, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 18, 18, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0094/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 95. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-20,"b":21,"scale":20,"offset":19}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -20, 21, 20, 19, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -20, 21, 20, 19, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0095/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 96. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-21,"b":22,"scale":21,"offset":20}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -21, 22, 21, 20, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -21, 22, 21, 20, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0096/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 97. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":21,"b":21,"scale":22,"offset":-21}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 21, 21, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 21, 21, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0097/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 98. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"jump_at_zero","a":-23,"b":24,"scale":23,"offset":22}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(jump_at_zero, -23, 24, 23, 22, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)

Wave6第四層核對=(jump_at_zero, -23, 24, 23, 22, 否, 否, 否, endpoint_interval_continuity_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0098/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 99. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"cusp_at_zero","a":-24,"b":25,"scale":24,"offset":23}。請依 [mode, a, b, scale, offset, closed_interval_continuity, open_interval_differentiability, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(cusp_at_zero, -24, 25, 24, 23, 是, 否, 否, open_interval_differentiability_fails_at_zero)

Wave6第四層核對=(cusp_at_zero, -24, 25, 24, 23, 是, 否, 否, open_interval_differentiability_fails_at_zero)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0099/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate





## 100. 微分中值定理

f(t)=A*t^2+B*t+C、a<b、closed interval continuity與open interval differentiability。操作=mvt-failure-boundary；資料={"mode":"degenerate_interval","a":24,"b":24,"scale":25,"offset":-24}。請依 [mode, a, b, ordered_endpoints, secant_slope_or_null, theorem_applicability, boundary] 欄序回答。

欄序由原始mode選取：degenerate_interval有7欄，jump_at_zero／cusp_at_zero有9欄；不補空欄，也不從答案形狀猜模式。null保留未提供的割線值，否表示此前提不足以套定理。

查看答案與解釋(degenerate_interval, 24, 24, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)

Wave6第四層核對=(degenerate_interval, 24, 24, 否, null, 否, a_less_than_b_and_nonzero_secant_denominator_required)；依完整明示資料獨立重算；witness c必須嚴格位於(a,b)且導數等於exact secant slope；witness不必唯一；有限samples、a=b、jump或interior cusp不可套定理。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261110-r02-mean-value-theorem-0100/)

微分中值定理 · qf-mod41-mvt-failure-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261110-r02-mean-value-theorem-foundations/validation-report.json)