微分中值定理的证明及应用中的辅助函数构造

微分中值定理是微分学的基础内容,也是用来研究函数性态的重要手段.因此,对微分中值定理的研究和再证明长期以来都是经久不衰的话题.通过对微分中值定理的再证明,不仅有利于初学者对定理的理解和掌握,也有利于其对定理的灵活运用,同时通过对微分中值定理的推广,还可以得到更加一般的情形.

The Structure of Auxiliary Functions in Certification and Applications of Differential Mean Value Theorem

The differential mean value theorem is the basic content of differential calculus, and an important way to study the state of function. Therefore, for a long time, the research and improving on the differential mean value theorem is an enduring topic. It is not only helpful to the beginners to understand and master the theorem, but also to apply the theorem flexibly by reproving the differential mean value theorem. Meanwhile, we can obtain more general cases by extending the differential mean value theorem.