# 介值定理基礎 · 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-20261015-advance-20261116-r02-intermediate-value-theorem-foundations · 2026-10-15 · 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. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[12,1],"a":-13,"b":-11,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([12, 1], -13, -11, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([12, 1], -13, -11, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0001/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 2. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[11,1],"a":-12,"b":-10,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([11, 1], -12, -10, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([11, 1], -12, -10, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0002/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 3. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[10,1],"a":-11,"b":-9,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([10, 1], -11, -9, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([10, 1], -11, -9, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0003/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 4. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[9,1],"a":-10,"b":-8,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([9, 1], -10, -8, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([9, 1], -10, -8, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0004/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 5. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[8,1],"a":-9,"b":-7,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([8, 1], -9, -7, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([8, 1], -9, -7, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0005/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 6. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[7,1],"a":-8,"b":-6,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([7, 1], -8, -6, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([7, 1], -8, -6, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0006/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 7. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[6,1],"a":-7,"b":-5,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([6, 1], -7, -5, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([6, 1], -7, -5, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0007/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 8. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[5,1],"a":-6,"b":-4,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([5, 1], -6, -4, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([5, 1], -6, -4, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0008/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 9. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[4,1],"a":-5,"b":-3,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([4, 1], -5, -3, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([4, 1], -5, -3, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0009/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 10. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[3,1],"a":-4,"b":-2,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

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

Wave6第十層核對=([3, 1], -4, -2, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0010/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 11. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[2,1],"a":-3,"b":-1,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([2, 1], -3, -1, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([2, 1], -3, -1, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0011/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 12. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[1,1],"a":-2,"b":0,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([1, 1], -2, 0, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([1, 1], -2, 0, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0012/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 13. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[0,1],"a":-1,"b":1,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([0, 1], -1, 1, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([0, 1], -1, 1, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0013/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 14. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-1,1],"a":0,"b":2,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-1, 1], 0, 2, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-1, 1], 0, 2, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0014/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 15. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-2,1],"a":1,"b":3,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-2, 1], 1, 3, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-2, 1], 1, 3, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0015/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 16. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-3,1],"a":2,"b":4,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

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

Wave6第十層核對=([-3, 1], 2, 4, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0016/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 17. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-4,1],"a":3,"b":5,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-4, 1], 3, 5, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-4, 1], 3, 5, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0017/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 18. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-5,1],"a":4,"b":6,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-5, 1], 4, 6, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-5, 1], 4, 6, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0018/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 19. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-6,1],"a":5,"b":7,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-6, 1], 5, 7, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-6, 1], 5, 7, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0019/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 20. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-7,1],"a":6,"b":8,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-7, 1], 6, 8, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-7, 1], 6, 8, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0020/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 21. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-8,1],"a":7,"b":9,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-8, 1], 7, 9, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-8, 1], 7, 9, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0021/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 22. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-9,1],"a":8,"b":10,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-9, 1], 8, 10, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-9, 1], 8, 10, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0022/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 23. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-10,1],"a":9,"b":11,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-10, 1], 9, 11, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-10, 1], 9, 11, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0023/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 24. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-11,1],"a":10,"b":12,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-11, 1], 10, 12, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-11, 1], 10, 12, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0024/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 25. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-hypothesis；資料={"coefficients":[-12,1],"a":11,"b":13,"target":0}。請依 [coefficients, a, b, value_at_a, value_at_b, target, polynomial_continuous, inclusive_bracket, certificate] 欄序回答。

查看答案與解釋([-12, 1], 11, 13, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)

Wave6第十層核對=([-12, 1], 11, 13, -1, 1, 0, 是, 是, polynomial_continuity_plus_inclusive_endpoint_bracket)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0025/)

介值定理 · qf-mod47-ivt-hypothesis · candidate





## 26. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[12,1],"a":-13,"b":-11,"target":0,"root":-12}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-12, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-12, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0026/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 27. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[11,1],"a":-12,"b":-10,"target":0,"root":-11}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-11, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-11, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0027/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 28. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[10,1],"a":-11,"b":-9,"target":0,"root":-10}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-10, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-10, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0028/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 29. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[9,1],"a":-10,"b":-8,"target":0,"root":-9}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-9, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-9, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0029/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 30. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[8,1],"a":-9,"b":-7,"target":0,"root":-8}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-8, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-8, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0030/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 31. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[7,1],"a":-8,"b":-6,"target":0,"root":-7}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-7, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-7, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0031/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 32. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[6,1],"a":-7,"b":-5,"target":0,"root":-6}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-6, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-6, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0032/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 33. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[5,1],"a":-6,"b":-4,"target":0,"root":-5}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-5, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-5, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0033/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 34. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[4,1],"a":-5,"b":-3,"target":0,"root":-4}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-4, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-4, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0034/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 35. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[3,1],"a":-4,"b":-2,"target":0,"root":-3}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-3, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-3, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0035/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 36. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[2,1],"a":-3,"b":-1,"target":0,"root":-2}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-2, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-2, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0036/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 37. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[1,1],"a":-2,"b":0,"target":0,"root":-1}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(-1, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(-1, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0037/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 38. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[0,1],"a":-1,"b":1,"target":0,"root":0}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(0, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(0, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0038/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 39. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-1,1],"a":0,"b":2,"target":0,"root":1}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(1, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(1, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0039/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 40. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-2,1],"a":1,"b":3,"target":0,"root":2}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(2, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(2, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0040/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 41. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-3,1],"a":2,"b":4,"target":0,"root":3}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(3, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(3, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0041/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 42. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-4,1],"a":3,"b":5,"target":0,"root":4}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(4, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(4, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0042/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 43. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-5,1],"a":4,"b":6,"target":0,"root":5}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(5, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(5, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0043/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 44. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-6,1],"a":5,"b":7,"target":0,"root":6}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(6, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(6, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0044/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 45. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-7,1],"a":6,"b":8,"target":0,"root":7}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(7, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(7, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0045/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 46. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-8,1],"a":7,"b":9,"target":0,"root":8}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(8, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(8, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0046/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 47. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-9,1],"a":8,"b":10,"target":0,"root":9}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(9, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(9, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0047/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 48. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-10,1],"a":9,"b":11,"target":0,"root":10}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(10, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(10, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0048/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 49. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-11,1],"a":10,"b":12,"target":0,"root":11}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(11, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(11, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0049/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 50. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-exact-root；資料={"coefficients":[-12,1],"a":11,"b":13,"target":0,"root":12}。請依 [root, value_at_root, inside_closed_interval, hits_target, uniqueness_or_closed_form_claim, certificate] 欄序回答。

查看答案與解釋(12, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)

Wave6第十層核對=(12, 0, 是, 是, 否, IVT_existence_does_not_imply_uniqueness_or_rational_closed_form)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0050/)

介值定理 · qf-mod47-ivt-exact-root · candidate





## 51. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[13,1],"a":-13,"b":-11,"target":0,"root":-13}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-13, -11, 0, -13, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-13, -11, 0, -13, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0051/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 52. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[12,1],"a":-12,"b":-10,"target":0,"root":-12}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-12, -10, 0, -12, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-12, -10, 0, -12, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0052/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 53. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[11,1],"a":-11,"b":-9,"target":0,"root":-11}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-11, -9, 0, -11, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-11, -9, 0, -11, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0053/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 54. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[10,1],"a":-10,"b":-8,"target":0,"root":-10}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-10, -8, 0, -10, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-10, -8, 0, -10, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0054/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 55. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[9,1],"a":-9,"b":-7,"target":0,"root":-9}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-9, -7, 0, -9, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-9, -7, 0, -9, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0055/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 56. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[8,1],"a":-8,"b":-6,"target":0,"root":-8}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-8, -6, 0, -8, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-8, -6, 0, -8, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0056/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 57. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[7,1],"a":-7,"b":-5,"target":0,"root":-7}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-7, -5, 0, -7, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-7, -5, 0, -7, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0057/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 58. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[6,1],"a":-6,"b":-4,"target":0,"root":-6}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-6, -4, 0, -6, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-6, -4, 0, -6, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0058/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 59. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[5,1],"a":-5,"b":-3,"target":0,"root":-5}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-5, -3, 0, -5, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-5, -3, 0, -5, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0059/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 60. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[4,1],"a":-4,"b":-2,"target":0,"root":-4}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-4, -2, 0, -4, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-4, -2, 0, -4, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0060/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 61. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[3,1],"a":-3,"b":-1,"target":0,"root":-3}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-3, -1, 0, -3, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-3, -1, 0, -3, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0061/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 62. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[2,1],"a":-2,"b":0,"target":0,"root":-2}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-2, 0, 0, -2, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-2, 0, 0, -2, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0062/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 63. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[1,1],"a":-1,"b":1,"target":0,"root":-1}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(-1, 1, 0, -1, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(-1, 1, 0, -1, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0063/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 64. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[0,1],"a":0,"b":2,"target":0,"root":0}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(0, 2, 0, 0, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(0, 2, 0, 0, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0064/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 65. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-1,1],"a":1,"b":3,"target":0,"root":1}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(1, 3, 0, 1, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(1, 3, 0, 1, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0065/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 66. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-2,1],"a":2,"b":4,"target":0,"root":2}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(2, 4, 0, 2, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(2, 4, 0, 2, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0066/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 67. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-3,1],"a":3,"b":5,"target":0,"root":3}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(3, 5, 0, 3, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(3, 5, 0, 3, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0067/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 68. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-4,1],"a":4,"b":6,"target":0,"root":4}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(4, 6, 0, 4, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(4, 6, 0, 4, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0068/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 69. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-5,1],"a":5,"b":7,"target":0,"root":5}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(5, 7, 0, 5, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(5, 7, 0, 5, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0069/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 70. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-6,1],"a":6,"b":8,"target":0,"root":6}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(6, 8, 0, 6, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(6, 8, 0, 6, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0070/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 71. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-7,1],"a":7,"b":9,"target":0,"root":7}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(7, 9, 0, 7, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(7, 9, 0, 7, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0071/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 72. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-8,1],"a":8,"b":10,"target":0,"root":8}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(8, 10, 0, 8, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(8, 10, 0, 8, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0072/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 73. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-9,1],"a":9,"b":11,"target":0,"root":9}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(9, 11, 0, 9, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(9, 11, 0, 9, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0073/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 74. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-10,1],"a":10,"b":12,"target":0,"root":10}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(10, 12, 0, 10, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(10, 12, 0, 10, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0074/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 75. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-endpoint-bracket；資料={"coefficients":[-11,1],"a":11,"b":13,"target":0,"root":11}。請依 [a, b, target, root, root_is_endpoint, inclusive_bracket, root_certificate, certificate] 欄序回答。

查看答案與解釋(11, 13, 0, 11, 是, 是, 是, endpoints_are_included)

Wave6第十層核對=(11, 13, 0, 11, 是, 是, 是, endpoints_are_included)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0075/)

介值定理 · qf-mod47-ivt-endpoint-bracket · candidate





## 76. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":1}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-1_for_x<0_and_1_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-1_for_x<0_and_1_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0076/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 77. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":2}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=2*x, 0, 1, 4, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=2*x, 0, 1, 4, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0077/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 78. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":3}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -3, 3, 9, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -3, 3, 9, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0078/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 79. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":4}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-4_for_x<0_and_4_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-4_for_x<0_and_4_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0079/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 80. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":5}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=5*x, 0, 1, 10, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=5*x, 0, 1, 10, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0080/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 81. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":6}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -6, 6, 36, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -6, 6, 36, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0081/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 82. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":7}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-7_for_x<0_and_7_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-7_for_x<0_and_7_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0082/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 83. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":8}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=8*x, 0, 1, 16, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=8*x, 0, 1, 16, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0083/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 84. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":9}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -9, 9, 81, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -9, 9, 81, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0084/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 85. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":10}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-10_for_x<0_and_10_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-10_for_x<0_and_10_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0085/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 86. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":11}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=11*x, 0, 1, 22, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=11*x, 0, 1, 22, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0086/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 87. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":12}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -12, 12, 144, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -12, 12, 144, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0087/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 88. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":13}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-13_for_x<0_and_13_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-13_for_x<0_and_13_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0088/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 89. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":14}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=14*x, 0, 1, 28, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=14*x, 0, 1, 28, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0089/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 90. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":15}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -15, 15, 225, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -15, 15, 225, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0090/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 91. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":16}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-16_for_x<0_and_16_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-16_for_x<0_and_16_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0091/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 92. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":17}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=17*x, 0, 1, 34, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=17*x, 0, 1, 34, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0092/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 93. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":18}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -18, 18, 324, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -18, 18, 324, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0093/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 94. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":19}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-19_for_x<0_and_19_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-19_for_x<0_and_19_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0094/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 95. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":20}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=20*x, 0, 1, 40, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=20*x, 0, 1, 40, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0095/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 96. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":21}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -21, 21, 441, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -21, 21, 441, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0096/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 97. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":22}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-22_for_x<0_and_22_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-22_for_x<0_and_22_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0097/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 98. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonbracket","scale":23}。請依 [mode, function_description, a, b, target, inclusive_bracket, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonbracket, f(x)=23*x, 0, 1, 46, 否, 否)

Wave6第十層核對=(nonbracket, f(x)=23*x, 0, 1, 46, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0098/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 99. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"nonunique","scale":24}。請依 [mode, function_description, a, b, target, inclusive_bracket, multiplicity_statement, uniqueness_claim] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(nonunique, f(x)=x^2, -24, 24, 576, 是, two_roots_possible, 否)

Wave6第十層核對=(nonunique, f(x)=x^2, -24, 24, 576, 是, two_roots_possible, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0099/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate





## 100. 介值定理

a<b、continuous interval function與inclusive target bracket責任。操作=ivt-discontinuity-boundary；資料={"mode":"discontinuous_jump","scale":25}。請依 [mode, function_description, a, b, target, inclusive_bracket, continuous, root_exists] 欄序回答。

三種mode為8/7/8欄：jump無root；nonbracket不滿足bracket；nonunique有兩個endpoint roots。最後否在不同branch的角色不同，不得用arity猜選。

查看答案與解釋(discontinuous_jump, f(x)=-25_for_x<0_and_25_for_x>=0, -1, 1, 0, 是, 否, 否)

Wave6第十層核對=(discontinuous_jump, f(x)=-25_for_x<0_and_25_for_x>=0, -1, 1, 0, 是, 否, 否)；依完整明示資料獨立重算；exact root witness只證存在且endpoint允許；不保證unique或closed form；discontinuous sign change與finite samples不能套IVT。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261116-r02-intermediate-value-theorem-0100/)

介值定理 · qf-mod47-ivt-discontinuity-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261116-r02-intermediate-value-theorem-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261116-r02-intermediate-value-theorem-foundations/validation-report.json)