摘要:微分中值定理主要包括罗尔定理，拉格朗日中值定理和柯西中值定理，它建立了函数值与导数值之间的定量联系,是整个微分学的理论基础。本文主要简单论述微分中值定理的具体内容，从而总结各定理之间的联系以及区别，再对各定理加以适当推广得到一些特殊结论。最后从导函数零点的存在性，辅助函数构造方法，证明不等式等方面讨论微分中值定理的应用。

关键词：罗尔定理； 拉格朗日中值定理； 柯西中值定理；导函数

Abstract:Differential mean value theorem includes Roll Theorem, the Lagrange Theorem and Cauchy Theorem, it builds the fixed contraction between function value and derivatives and it is the differential calculus's theoretical basis. This paper clarifies the content of the differential mean value theorem, so as to understand the link and the distinction between the theorems. Then, it extends the theorems and gets some special conclusions. Finally, it discusses the application of differential mean value theorem from the Zero of derivative theorem ,  the construct method of auxiliary function and the proof of inequality and so on .

Key words: Roll Theorem; Lagrange Theorem; Cauchy Theorem; Derivative Function