In solving mathematical problems, a

In solving mathematical problems, auxiliary functions have high application value, at present, most of the textbooks or reference materials are directly given auxiliary functions, so only need to be analyzed around this, you can find the laws that exist. Take, for example, the proof of Lagrange's median theorem and Cauchy's median theorem, both of which apply auxiliary functions. Of course, the constructors of auxiliary functions are divided into many kinds, and depending on the form, the constructed auxiliary functions must be different. Therefore, the construction method and applied research of auxiliary functions in the differential median theorem have important significance