分段函数在分段点处可导性的判别方法  

A Method of Judging the Differentiability of Piecewise Functions at Segment Point

作　　者：王银坤 倪谷炎[1] WANG Yinkun;NI Guyan(Department of Mathematics,College of Sciences,National University of Defense Technology,Changsha 410072,China)

机构地区：[1]国防科技大学理学院数学系,长沙410072

出　　处：《大学数学》2023年第1期67-71,共5页College Mathematics

基　　金：国家自然科学基金(11871472);湖南省自然科学基金(2022JJ40541);国防科技大学校预研项目(ZK19-19)。

摘　　要：针对高等数学课程中分段函数可导性问题,基于函数可微的概念和泰勒公式给出一种新的分段函数在分段点处可导性的判别方法.该方法不需按照导数定义计算分段点处的导数,也不需求导函数在分段点处的极限.与它们相比,该方法更简单,同时加深了对可微概念的理解.Aiming at the problem of the differentiability of piecewise functions in the course of Advanced Mathematics,a new method for judging the differentiability of the piecewise function at the piecewise point is given based on the concept of function differentiability and Taylor's formula.This method does not need to calculate the derivative at the segment point according to the derivative definition,nor does it require the limit of the derivative function at the segment point.Compared with them,this method is simpler and deepens the understanding of the differentiable concept.

关 键 词：分段函数 导数 泰勒公式 

分 类 号：O177.5[理学—数学]