第 29928 題：由明示錨點解原函數常數

原題與已知條件

全實數論域；升冪係數的受限多項式模型。升冪係數 f=[-10, 3, 1, 3]，F0常數項固定零。令 F=F0+C 且 F(-3)=-10/3，求C。

• G001 — 全實數論域；升冪係數的受限多項式模型。升冪係數 f=[-10, 3, 1, 3]，F0常數項固定零。令 F=F0+C 且 F(-3)=-10/3，求C。

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-antiderivative

逐步推導

source roles = [qf-density-primitive-anchor-constant, density_primitive_anchor_constant]

derived = [[required_additive_constant_fraction_retaining1]]

source roles = [integrand f, [-10, 3, 1, 3], 否]

derived = [[-10/1, 3/1, 1/1, 3/1]]

Primitive ORIGINAL coefficient degree1 := div(-10, 1)

Primitive ORIGINAL coefficient degree1 = -10

Primitive ORIGINAL coefficient degree2 := div(3, 2)

Primitive ORIGINAL coefficient degree2 = 3/2

Primitive ORIGINAL coefficient degree3 := div(1, 3)

Primitive ORIGINAL coefficient degree3 = 1/3

Primitive ORIGINAL coefficient degree4 := div(3, 4)

Primitive ORIGINAL coefficient degree4 = 3/4

Primitive reverse ORIGINAL derivative coefficient0 := mul(-10, 1)

Primitive reverse ORIGINAL derivative coefficient0 = -10

Primitive reverse ORIGINAL derivative coefficient1 := mul(3/2, 2)

Primitive reverse ORIGINAL derivative coefficient1 = 3

Primitive reverse ORIGINAL derivative coefficient2 := mul(1/3, 3)

Primitive reverse ORIGINAL derivative coefficient2 = 1

Primitive reverse ORIGINAL derivative coefficient3 := mul(3/4, 4)

Primitive reverse ORIGINAL derivative coefficient3 = 3

source roles = [[-10/1, 3/1, 1/1, 3/1]]

derived = [[0/1, -10/1, 3/2, 1/3, 3/4], [-10/1, 3/1, 1/1, 3/1], 是]

Primitive anchor ORIGINAL Horner product degree4 := mul(0, -3)

Primitive anchor ORIGINAL Horner product degree4 = 0

Primitive anchor ORIGINAL Horner sum degree4 := sum(0, 3/4)

Primitive anchor ORIGINAL Horner sum degree4 = 3/4

Primitive anchor ORIGINAL Horner product degree3 := mul(3/4, -3)

Primitive anchor ORIGINAL Horner product degree3 = -9/4

Primitive anchor ORIGINAL Horner sum degree3 := sum(-9/4, 1/3)

Primitive anchor ORIGINAL Horner sum degree3 = -23/12

Primitive anchor ORIGINAL Horner product degree2 := mul(-23/12, -3)

Primitive anchor ORIGINAL Horner product degree2 = 23/4

Primitive anchor ORIGINAL Horner sum degree2 := sum(23/4, 3/2)

Primitive anchor ORIGINAL Horner sum degree2 = 29/4

Primitive anchor ORIGINAL Horner product degree1 := mul(29/4, -3)

Primitive anchor ORIGINAL Horner product degree1 = -87/4

Primitive anchor ORIGINAL Horner sum degree1 := sum(-87/4, -10)

Primitive anchor ORIGINAL Horner sum degree1 = -127/4

Primitive anchor ORIGINAL Horner product degree0 := mul(-127/4, -3)

Primitive anchor ORIGINAL Horner product degree0 = 381/4

Primitive anchor ORIGINAL Horner sum degree0 := sum(381/4, 0)

Primitive anchor ORIGINAL Horner sum degree0 = 381/4

Primitive anchor ORIGINAL target minus F0 at anchor := sub(-10/3, 381/4)

Primitive anchor ORIGINAL target minus F0 at anchor = -1183/12

Primitive anchor reverse SAME F0 value plus C := sum(381/4, -1183/12)

Primitive anchor reverse SAME F0 value plus C = -10/3

source roles = [[-10/1, 3/1, 1/1, 3/1], -3, -10/3, [0/1, -10/1, 3/2, 1/3, 3/4]]

derived = [381/4, -1183/12, -10/3, 是]

逐步反向核對

• S024 · premise_and_result_audit — 反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。
• S023 · premise_and_result_audit — 以精確有理數重算 Primitive anchor reverse SAME F0 value plus C，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL target minus F0 at anchor，不以小數近似替代。
• S021 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner sum degree0，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner product degree0，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner sum degree1，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner product degree1，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner sum degree2，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner product degree2，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner sum degree3，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner product degree3，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner sum degree4，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 Primitive anchor ORIGINAL Horner product degree4，不以小數近似替代。
• S011 · premise_and_result_audit — 反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。
• S010 · premise_and_result_audit — 以精確有理數重算 Primitive reverse ORIGINAL derivative coefficient3，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 Primitive reverse ORIGINAL derivative coefficient2，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 Primitive reverse ORIGINAL derivative coefficient1，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 Primitive reverse ORIGINAL derivative coefficient0，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 Primitive ORIGINAL coefficient degree4，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 Primitive ORIGINAL coefficient degree3，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 Primitive ORIGINAL coefficient degree2，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 Primitive ORIGINAL coefficient degree1，不以小數近似替代。
• S002 · premise_and_result_audit — 反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。
• S001 · premise_and_result_audit — 反向逐項代回原題資料、同一索引／方向／代表式與本步前提；不只核答案。精確候選核對、獨立審查、形式證明與發布資格仍分開。

結論

-1183/12

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。