微分中值定理的另类证明与应用  

The Different Proofs of the Differential Mean Value Theorem and Its Application

作　　者：王秀玲[1] 

机构地区：[1]宿迁高等师范学校数学系,江苏宿迁223800

出　　处：《安庆师范学院学报（自然科学版）》2010年第4期93-95,共3页Journal of Anqing Teachers College(Natural Science Edition)

摘　　要：在通常的数学分析教材中,微分中值定理的证明是通过构造辅助函数,在罗尔中值定理的基础上证明的。受到Darboux定理的证明方法的启发,本文给出了构造另类辅助函数,应用罗尔中值定理证明微分中值定理的新方法,并介绍了微分中值定理在解决数学问题中的广泛应用。In the general mathematical analysis textbooks,the proof of the differential mean value theorem is built on the Rolle＇s theorem by means of constructing an auxiliary function.Inspired by the proof of Darboux Theorem,this paper gives two new ways to prove the Lagrange Mean Value and the Cauchy Mean Value Theorem where two different auxiliary functions are constructed and the Rolle＇s theorem is applied.Furthermore one introduces some application of the differential mean value theorems in solving mathematical problems.

关 键 词：微分中值定理 DARBOUX定理 辅助函数 

分 类 号：O172.1[理学—数学]