Cauchy微分中值定理证法思路探析

为了培养学生的数学思维,提高学生的创新能力,从多角度和多方位对Cauchy微分中值定理的证明方法进行了探讨,归纳出了利用罗尔定理、同增量性、单调性、行列式、定积分、复合函数等证明Cauchy微分中值定理的方法.利用分析法分析了构造适当辅助函数证明的思路.

On the Cauchy Differential Mean Value Theorem Proof Train of Thought

In order to cultivate the students mathematical thinking, and improve the innovative ability of students, an exploration is made into the proof methods for the Cauchy differential mean value theorem from multiple perspectives via allround approaches. Summed up are the proof methods for the Cauchy differential mean value theorem by aid of the Rolle＇s theorem, increment, monotonicity, Cauchy determinant, definite integral and complex function. Using the analytical method, the train of thought by constructing certain auxiliary functions is also subjected to a detailed examination.