Methods and Skills of Solving Several Kinds of Differential Mean Value Theorem Proving Problems

Abstract

The differential mean value theorem is one of the important basic theorems in differential calculus and a powerful tool to study the properties of the Han script. It reflects the relationship between functions and derivatives. Many proof questions encountered in the study of calculus need to use the relevant knowledge of the differential mean value theorem, and students are often at a loss. In this paper, several types of differential mean value theorems are discussed in depth, and it is found that the key point and difficulty in proving many propositions related to differential mean value theorems is to construct appropriate auxiliary functions. By constructing auxiliary functions, abstract and seemingly unrelated conclusions can be transformed into relatively straightforward views, which can easily find the path that meets the conditions of differential mean value theorems, and then solve the problem. Through these types of questions, this paper summarizes the common skills to find auxiliary functions, hoping to provide some help for students in learning, postgraduate entrance examination, etc.