多个函数多介值的微分中值定理及其应用

Differential Mean Value Theorem of Multiple Functions and Multiple Mean Values and Its Application

基于Rolle定理、Lagrange中值定理和Cauchy中值定理,从多个函数的角度出发,对微分中值定理进行推广,给出了关于三个函数的微分中值定理,得到了多个函数多介值的微分中值定理的新形式,拓展了微分中值定理的应用范围。

In this paper,the differential mean value theorem is generalized based on Rolle's theorem,Lagrange's mean value theorem and Cauchy's mean value theorem.From the perspective of multiple functions,the differential mean value theorem for three functions is given and a new form of differential mean value theorem with multiple functions and multiple mean values is obtained,which extends the application range of the differential mean value theorem.