Study on the Relations and Differences of Differential Mean Value Theorems

The differential mean value theorem plays an important role in the differential calculus.In this paper, by comparing and analyzing the premise conditions and conclusions of three differential mean value theorems, we discuss the similarities and differences between them at first.Then, according to different principles, we summarize two kinds of typical methods of proving Lagrange's theorem and Cauchy's theorem which will be helpful for readers to understand the differential mean value theorems.