高师理科学刊Issue(9)：75-78,4.DOI:10.3969/j.issn.1007-9831.2015.09.022
罗尔定理应用中辅助函数的构造
The construction of auxiliary functions using Rolle′s theorem
卢刚夫1
作者信息
- 1. 山东理工大学理学院，山东淄博 255049
- 折叠
摘要
Abstract
When applying Rolle′s theorem to prove mathematical problems, constructing a problem-related auxiliary function is one of the most common ways,which is not only necessary but critical for the mathematical proof.However,the construction of auxiliary functions usually doesn′t have fixed patterns and methods but needs skillful techniques.It is a key content and difficult point during the process of learning and teaching advanced mathematics.Discussed five common used methods for constructing the auxiliary function when applying Rolle′s theorem,including primitive function method,multiplication factor method,indefinite integration method, differential equation method and constantk-value method.With the help of in-depth understanding of those methods,proposed some guiding principles for the construction of auxiliary functions when using Rolle′s theorem, which provide insights for teaching and learning advanced mathematics in practice.关键词
罗尔定理/辅助函数/构造方法Key words
Rolle′s theorem/auxiliary function/construction method分类
数理科学引用本文复制引用
卢刚夫..罗尔定理应用中辅助函数的构造[J].高师理科学刊,2015,(9):75-78,4.
