拉格朗日中值定理的结构分析及其应用

Structure Analysis and Application of Lagrange Mean Value Theorem

拉格朗日中值定理是函数微分理论的核心内容,是研究函数高级分析性质的主要工具。通过对拉格朗日中值定理结构的分析,得出拉格朗日中值定理可以作用对象的结构特征,不仅解决了“如何用”拉格朗日中值定理的问题,更解决了“为什么能用”的问题,有利于帮助学生理解和掌握拉格朗日中值定理和题目之间的联系与应用。

Lagrange mean value theorem is the core content of function differential theory and the main tool to study the advanced analytical properties of function. Through the analysis of the structure of the Lagrange mean value theorem, it is concluded that the Lagrange mean value theorem can act on the structural characteristics of the object, which not only solves the problem of “how to use” the Lagrange mean value theorem, but also solves the problem of “why it can be used”, which is helpful to help students understand and master the relationship and application between the Lagrange mean value theorem and the problem.