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| 微分学中不等式的证明 | |
| 引用本文： | 杨黎霞. 微分学中不等式的证明[J]. 高等数学研究, 2011, 14(1): 56-59 |
| 作者姓名： | 杨黎霞 |
| 作者单位： | 江南大学,理学院,江苏,无锡214122 |
| 摘 要： | 针对微分学不等式列出五种常用证明方法,即利用单调性证明法,利用拉格朗日中值定理证明法,利用最值证明法,利用泰勒公式证明法,和利用凹凸性证明法.实例说明每种方法的使用细节,以达到使初学者能尽快掌握微分学不等式证明的目的. |
| 关 键 词： | 不等式 单调性 中值定理 凹凸性 |
Proofs of Inequalities by Derivatives |
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| YANG Li-xia. Proofs of Inequalities by Derivatives[J]. Studies In College Mathematics, 2011, 14(1): 56-59 | |
| Authors: | YANG Li-xia |
| Affiliation: | YANG Li-xia (School of Sciences, Jiangnan University, Wuxi 214122, PRC) |
| Abstract: | In this paper, common methods of proving inequalities by derivatives are summarized into five categories： monotonicity, differential mean-value theorem, maximum and minimum, Taylor formula, and concave-convex property. Using examples, we illustrate each method in details with the purpose of enabling learners to master the proof of inequalities by derivative quickly. |
| Keywords: | inequality monotonieity differential mean-value theorem concave-convex property |
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