摘要
从多角度对Cauchy中值定理的证明方法作了进一步探讨,归纳出了多种证明方法,其中包括利用Rolle定理证明,利用达布定理证明,利用同增量性定理证明,利用积分中值定理证明等七条路径.并利用反向分析法分析了如何构造出适当的辅助函数进行有效证明,有利于培养学生的数学思维,提高学生的创新能力。
Further discussion about the proof methods of Canchy mean value theorem is given from multiple perspectives, and a variety of proof methods are summarized , which includes using RoUe theorem, using Darboux theorem, using the same increment theorem and using mean value theorem. Moreover, by using inverse analysis method, this paper analyzes how to construct appropriate auxiliary function to effectively prove, which is beneficial to cultivating students＇ mathematical thinking and improving their innovative ability.
出处
《成都师范学院学报》
2013年第7期112-114,共3页
Journal of Chengdu Normal University
关键词
CAUCHY中值定理
证明
辅助函数
Cauchy mean value theorem
certification
auxiliary function
