辅助函数的构造

Construction of Auxiliary Function

多数微积分教材在证明时，采用辅助函数。但辅助函数如何构造出来的，并没有给出详细论证。研究了辅助函数的构造过程，找到了满足罗尔定理的辅助函数的条件，给出了另外几种辅助函数，并归纳为更一般的辅助函数。

Auxiliary functions are used to prove the Lagrange Theorem, in most text books. But, how to construct the auxiliary functions is not detailed. Considering the structure of the auxiliaty functions, I have found the condition of auxiliary function, meeting the Roll Theorem. Some other auxiliary functions are given. A more general auxiliary functionone is reduced.