| 微分中值定理及微分Darboux定理新证明方法 |
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| 引用本文： | 张琳,郭三刚. 微分中值定理及微分Darboux定理新证明方法[J]. 陕西理工学院学报(自然科学版), 2012, 28(2): 67-71 |
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| 作者姓名： | 张琳 郭三刚 |
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| 作者单位： | 陕西理工学院数学与计算机科学学院,陕西汉中,723000 |
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| 摘 要： | 给出了函数单调性判定定理的一种新证明方法,并由此给出了反函数的连续性、可导性和求导公式的严密证明,同时给出了微分中值定理和微分Darboux定理及其推广形式的一种新的简洁证明方法。
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| 关 键 词： | 单调性 反函数 连续性 可导性 微分中值定理 微分Darboux定理 |
New methods for proving the differential mean value theorems and differential Darboux theorem |
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| ZHANG Lin , GUO San-gang. New methods for proving the differential mean value theorems and differential Darboux theorem[J]. Journal of Shananxi University of Technology(Natural Science Edition), 2012, 28(2): 67-71 |
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| Authors: | ZHANG Lin GUO San-gang |
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| Affiliation: | (School of Mathematics and Computer Science,Shaanxi University of Technology, Hanzhong 723000,China) |
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| Abstract: | A novel method of proof of the theorem was proposed for judging the monotonicity of a differentiable function,by means of which,a more rigorous proof was presented of the continuity,differentiability and the derivative formulae of the inverse function,a succinct method for proving the differential mean value theorems and differential Darboux theorem and its extension was also given. |
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| Keywords: | monotonicity inverse function continuity differentiability differential mean value theorems differential Darboux theorem |
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