一道关于中值题目的证明方法探讨

Discussion on the Proof Method of a Problem of Median Value

对一道关于中值问题的证明题进行探讨,提出四种证明方法,即分别利用改进的积分中值定理、牛顿—莱布尼茨公式、罗尔定理和反证法对其予以证明.对中值问题证明题进行不同证明方法的探讨,对于学生发散思维的培养具有良好的促进作用.

This paper discusses the proof method of a problem of median value. Four ways are proposed： improved mean - value theorem, Newton - Leibniz formula, Rolle Theorem and reduction to absurdity. Discussion of different proof methods of such problems can facilitate the cultivation of students ’ divergent thinking.