| 微分中值定理证明方法的思考 |
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| 引用本文： | 程村.微分中值定理证明方法的思考[J].科教文汇,2014(30):38-39. |
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| 作者姓名： | 程村 |
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| 作者单位： | 北京工商大学理学院数学系 北京 100048 |
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| 摘 要： | 高等数学的教材是以罗尔定理为基础,通过引进适当满足罗尔定理的辅助函数去证明拉格朗日中值定理和柯西中值定理。本文将讨论如何构造辅助函数去证明拉格朗日中值定理和柯西中值定理。此外,本文还给出了证明微分中值定理的另外一种方法：辅助定理法。
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| 关 键 词： | 拉格朗日中值定理 柯西中值定理 罗尔定理辅助函数 |
Pondering on Methods to Prove the Differential Mean ;Value Theorem |
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| Authors: | Cheng Cun |
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| Abstract: | In advanced mathematics textbooks, it is based on the Rolle Theorem, by introducing an appropriate auxiliary function that satisfies the Rolle Theorem to prove the Lagrange Mean Value Theorem and the Cauchy Mean Value Theorem. This paper will discuss how to construct an auxiliary function to prove Lagrange Mean Value Theorem and Cauchy Mean Value Theorem.In addition, the paper also gives another method to prove the differential mean value theorem： Lemma method. |
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| Keywords: | Lagrange Mean Value Theorem Cauchy Mean Value Theorem Rolle Theorem auxiliary function |
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