第 22244 題：微分中值定理

原題與已知條件

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 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 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 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-mean-value-theorem

逐步推導

source operation=mvt-hypothesis-audit;original snapshot and mathematics retained

explicit ordered source output fields=[a, b, ordered_endpoints, closed_interval_continuity, open_interval_differentiability, certificate]

ORIGINAL WHOLE f(t)=(4)t^2+(8)t+(325);a=-20<b=21;all endpoint[Ax,Axx,Bx,Axx+Bx,Axx+Bx+C] rows=[[-80, 1600, -160, 1440, 1765], [84, 1764, 168, 1932, 2257]]

English source ALL endpoint intermediate SAFE guards passed;polynomial continuous on CLOSED[a,b] and differentiable on OPEN(a,b),not inferred from finite samples

逐步反向核對

• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(-20, 21, 是, 是, 是, polynomial_continuous_on_closed_interval_and_differentiable_on_open_interval)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。