导函数极限的存在性与函数可导性关系初探

在讨论函数在某一点的可导性时 ,通常的做法是利用导函数的定义或者用函数在该点的左、右导数来讨论 ,过程比较复杂。为了寻求一种简便的方法 ,总结出下面一组关于导函数极限的存在性与函数可导性间关系的命题 ,利用这两个命题 ,能使相应问题的讨论变得比较简单

Relation between existence of derivative function limit and derivation of function

It is the usual way to discuss the derivation of function at some point with the de finition of Derivative function or the left and right derivatives of Function at the certain point. It is very complicated and confused.In order to seek an easy and effective method,have summed up the following topics on the relations between the existence of derivative function Limit and derivation of functions .With the topics,the discussion about the problems concemed could thus become comparatively easier than ever before.