有限开区间上的柯西中值定理

Cauchy Differential Mean Value Theorem on Open Interval

通过给出一个反例,指出了文献[2]中有限开区间上柯西中值定理的错误,给出了有限开区间上的柯西中值定理,推广了柯西中值定理,使得利用导数研究开区间上函数的整体性态更为方便。

This paper presents the error of Cauchy differential mean value theorem on open interval in paper[ 2 ] by giving a counter example, then gives the correct Cauchy differential mean value theo- rem on open interval, which generalizes Cauchy differential mean value theorem and makes it more convenient to study general characters of functions defined on open interval by means of derivative.