微分中值定理的推广及应用

Generalization and Application of Differential Mean Value Theorem

微分中值定理是一系列中值定理的总称,是研究函数的有力工具.本文利用微分中值定理及闭区间上连续函数的性质,将原有的微分中值定理进行推广,给出新的微分中值定理,并通过实例说明新的中值定理的有效性.

The differential mean value theorem is a general term for a series of mean value theorems, and a powerful tool for studying functions. Using the differential mean value theorem and the properties of continuous functions on closed intervals, this paper is to generalize the original differential mean value theorem, and to construct a new differential mean value theorem whose validity is proved by examples.