The mean value Theorem, which revea

The mean value Theorem, which reveals the relations of functions at a certain point and in an interval, is an important tool for studying the properties of functions and has important theoretical significance and application value. In this paper, we prove the existence of root, the problem of containing median point, the continuity of function, the convergence of series, the calculation of limit and estimate, and the monotonicity of the function of the nine aspects of the mean value theorem. Using constructors and the method of constructing a mean value theorem form, the mean value theorem is applied to the proof, and some problems which do not contain mean value theorem form are solved, special forms are constructed through interval conditions and ranges of valto carry out reasoning proof