江西科学2025，Vol.43Issue(5)：894-897,4.DOI:10.13990/j.issn1001-3679.2025.05.012
函数f(x)在泰勒公式应用中的两个性质
Two Properties of the Function f(x)in the Application of Taylor's Formula
摘要
Abstract
This paper explores two interesting properties of the function f(x)in the applica-tion of Taylor's formula.It is proved that if f(x)has a finite(n-1)-th order derivative on R that is not identically constant and satisfies the specified conditions,then f(x)is a univari-ate n-th degree polynomial.Furthermore,if the parameter θ in the remainder term of the Taylor formula remains a constant,its value must be1/n.关键词
函数性质/泰勒公式/导数/多项式/常数θKey words
function properties/Taylor's formula/derivative/polynomial/constant θ分类
数理科学引用本文复制引用
彭蕾..函数f(x)在泰勒公式应用中的两个性质[J].江西科学,2025,43(5):894-897,4.基金项目
广州软件学院2024年度校级科研项目(KY202408). （KY202408）
