关于一道题目的思考——Rolle定理与积分中值定理的结合

Research on the Solution of a Class of Problem——A Combination of Rolle Theorem and Integral Mean Value Theorem

研究了一类常见题型的通用解法,从一道证明题出发联想到类似的许多题目,并就这些问题给出了一般的解法,即通过构造函数并利用Rolle中值定理和积分中值定理使问题得以证明.这个过程展现了数学中从最基本的问题出发,通过类比、归纳、总结得到一般性的规律.该方法具有一定的可操作性及参考价值,可使复杂题目简单化,从而达到触类旁通和举一反三的目的.

In this paper,the author makes a research of a common solution on questions which are frequently asked.The paper starts from a proof of a problem and makes association with a number of similar questions.Then,the paper gives a general solution of the questions by constructing the function and using Rolle Theorem and Integral Mean Value Theorem to prove the question.