| 有关中值定理的探究性教学 |
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| 引用本文： | 杨宪立,闫德明.有关中值定理的探究性教学[J].数学学习,2011(5):33-35. |
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| 作者姓名： | 杨宪立 闫德明 |
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| 作者单位： | 河南教育学院数学系,河南郑州450046 |
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| 基金项目： | 河南省教育科学“十一五”规划课题（2009-JKGHAG-0227）. |
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| 摘 要： | 通过对中值定理教学思路的设计，给出探究性教学方法的一个实例，即通过导数概念的物理意义导出Lagrange中值定理，经特殊化后推出Rolle定理，再经化归思想给出Lagrange定理的证明，最后推广得到Cauchy中值定理，并借助类比或化归思想分别给出Cauchy定理的证明．
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| 关 键 词： | 中值定理 化归 类比 辅助函数 |
Inquiry Teaching for Mean Value Theorem |
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| YANG Xian-li,YAN De-ming.Inquiry Teaching for Mean Value Theorem[J].Studies In College Mathematics,2011(5):33-35. |
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| Authors: | YANG Xian-li YAN De-ming |
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| Institution: | (Department of Mathematics, Henan Institute of Education, Zhengzhou 450046, PRC) |
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| Abstract: | A case of inquiry teaching is designed for the mean value theorem with the following steps. The Lagrange mean value theorem is first introduced by the interpretation of the concept of derivative, and then Rollers theorem which can be view as a special case of the Lagrange mean value theorem. The proof of the Lagrange mean value theorem is given by the reduction method. The Cauchy mean value theorem is introduced by generalizing the Lagrange mean value theorem, which is then proved by the analogy method or the reduction method. |
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| Keywords: | mean Value theorem reduction analogy auxiliary function |
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