微分中值定理及其应用

Mean Value Theorem and Its ApplicationsAbstract In this article,the course of the development of the differential mean theoremis presented,the specific content and the method of proof of the differential mean theoremare described,and the geometric meaning and the internal relationships of the threetheorems are described.Then some properties related to the theorem are explained.And.illustrates the application of the theorem using examples to further explore the relationshipbetween the function and the derived function.The combination of university teachingmaterials and collected examples fully shows the applicability of the differential meantheorem.The sentence is a relationship rope between the relationship function andderivative function.We often examine the properties of the function itself based on theproperties of the derivative function in the interval.We analyze the relationship betweenthe differential mean sets from content,form,mathematical meaning and proof of the setand show their theoretical value and important meaning.Key words Differential median theorem,Rolle's theorem,Lagrange mediantheorem,Cauchy median theorem,constructor