Differential Mean ValueTheorem In Middle School Mathematics

Differential mean value theorem, as basic theorem of differential calculus, plays a vital role between function and its derivatives. In this paper, we firstly describe the historical development of the differential mean value theorem, and introduce three kinds of common mean value theorems such as Rolle mean value theorem, Lagrange mean value theorem and Cauchy mean value theorem,and those theorems are discussed. Secondly, some different proof methods and generalizations of those differential mean value theorems are summarized.Thirdly,a large number of examples are given for specific application of the differential mean value theorems in solving different problems; At last, some applications of mean value theorem are summed up by combining the mathematics teaching practice in Senior High school.