| 广义微分中值定理 |
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| 引用本文： | 刘元会,常安定,邓秋霞.广义微分中值定理[J].纺织高校基础科学学报,2003,16(4):294-297. |
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| 作者姓名： | 刘元会 常安定 邓秋霞 |
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| 作者单位： | 1. 长安大学,理学院,陕西,西安,710064
2. 武警工程学院,通信工程系,陕西,西安,710086 |
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| 摘 要： | 对于k阶可导函数,利用拉格朗日中值定理,证明了函数的k阶导数与函数值之间的关系;对于s阶可导函数(s>k),证明了函数的s-k阶导数值与函数的s阶导数之间的关系.给出了常见的k=2,k=3,k=4对应的定理及其证明.
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| 关 键 词： | 高阶导数 中值定理 微分 |
| 文章编号： | 1006-8341(2003)04-0294-04 |
| 修稿时间： | 2003年9月2日 |
The generalized differential mean value theroem |
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| LIU Yuan-hui,CHANG An-ding,DENG Qiu-xia.The generalized differential mean value theroem[J].Basic Sciences Journal of Textile Universities,2003,16(4):294-297. |
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| Authors: | LIU Yuan-hui CHANG An-ding DENG Qiu-xia |
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| Abstract: | To the functions k-th derived,the relation between the values of the functions and the value of the k-th derived functions has been proved suing the lagrange mean value theorem. To the functions s-th derived (s>k) ,the relation between the values of the (s - k)-th derived functions and the value of the k-th derived functions has been given. To the situations k =2,3,4, according to the theorem above, the corresponding theorems have been given and proved. |
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| Keywords: | higher derivative the generalized mean value theorem differential |
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