| 曲线拐点充分条件证明中的常见错误 |
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| 引用本文： | 陈玉.曲线拐点充分条件证明中的常见错误[J].大学数学,2010,26(4). |
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| 作者姓名： | 陈玉 |
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| 摘 要： | 文1]给出了判别曲线拐点的两个充分条件,文2]给出了一个充分条件,但三个定理的证明都是错误的.同时,文1]的两个推论也是错误的.本文通过反例分析了其错因,并给出了文1]中一个拐点充分条件的正确证明.
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| 关 键 词： | 拐点 导数 凹函数 凸函数 |
The Common Errors in Proof of Sufficient Conditions of Judging Inflection Point |
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| CHEN Yu.The Common Errors in Proof of Sufficient Conditions of Judging Inflection Point[J].College Mathematics,2010,26(4). |
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| Authors: | CHEN Yu |
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| Abstract: | Two sufficient conditions in paper 1] and one sufficient condition in paper 2] are given to judge inflection point. But the proofs of them have mistakes and two corollaries in paper 1] are also wrong. This paper analyses the error reasons of them by some counter examples and gives a correct proof of one sufficient condition of paper 1]. |
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| Keywords: | inflection point derivative concave function convex function |
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