| 最值理论中一个结论的证明 |
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| 引用本文： | 李卫峰. 最值理论中一个结论的证明[J]. 高等数学研究, 2014, 0(5): 18-18 |
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| 作者姓名： | 李卫峰 |
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| 作者单位： | 中国地质大学武汉数学与物理学院,湖北武汉430074 |
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| 基金项目： | 中央高校基本科研业务费专项基金资助项目（CUGL110234） |
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| 摘 要： | 同济大学《高等数学》最值理论中有结论称“若一个函数在一个区间内可导且只有一个驻点，并且这个驻点是函数的极值点，那么此驻点也是该函数的最值点”，但并未给出证明。学生们对此频感好奇。受Fermat引理启发，利用反证法可获一个比此结论更为一般的定理。
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| 关 键 词： | 最值 极值 Femat引理 |
A Theorem about Global Extreme Value |
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| LI Weifeng. A Theorem about Global Extreme Value[J]. Studies In College Mathematics, 2014, 0(5): 18-18 |
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| Authors: | LI Weifeng |
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| Affiliation: | LI Weifeng (School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, PRC) |
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| Abstract: | “If a differentiable function on an interval has only one stationary point ,and the stationary point is a local extremum point of the function ,then the stationary point is also the global extremum point of the function”is a statement appeared ,without proof ,in the textbook of Higher Mathematics published by Tongji university . Students are usually curious about how to prove the result .In this paper ,inspired by Fermat’s lemma ,we establish a theorem ,which is more general than the result above . |
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| Keywords: | global extremum local extremum Femat’s lemma |
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