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微分中值定理是应用导数的局部性质研究函数在区间上整体性质的重要工具,是微分学的理论基础,在数学分析中处于十分重要的地位,同时在学习过程中也是较难理解和掌握的定理.本文力图通过对三个微分中值定理的几何解释,以及在证明过程中引入辅助函数的几何构思的辨析,帮助读者理解和认识这三个定理.
The differential mean value theorem is an important tool for studying the overall properties of the function in the interval using the local properties of the derivative. It is the theoretical basis of differential calculus and plays an important role in mathematical analysis. It is also difficult to understand and grasp in the learning process. Theorem. This paper attempts to help the reader understand and understand these three theorems by analyzing the geometry of the three differential mean value theorem and the geometric conception of auxiliary functions introduced in the proof process.