| 微分中值定理关系浅析 |
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| 引用本文： | 谈悦华,谢春娥.微分中值定理关系浅析[J].佛山科学技术学院学报(自然科学版),2006,24(3):8-10. |
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| 作者姓名： | 谈悦华 谢春娥 |
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| 作者单位： | 1. 广东省佛山市高级技工学校,广东,佛山,528000
2. 广州大学数学与信息科学学院,广东,广州,510006 |
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| 摘 要： | 从几何直观出发,立足于整体角度,研究微分中值定理之间的关系,讨论R o lle定理、L agrange定理、C auchy定理统一于微分学中值定理的各种形式;并以R o lle定理为基础,借助不同形式的辅助函数对其它微分中值定理作出多种形式的统一证明。
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| 关 键 词： | 微分中值定理 关系 统一 辅助函数 |
| 文章编号： | 1008-0171（2006）03-0008-03 |
| 收稿时间： | 2006-06-02 |
| 修稿时间： | 2006-06-02 |
An Analysis of the Relations in Differential Mean-value Theorems |
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| TAN Yue-hua,XIE Chun-e.An Analysis of the Relations in Differential Mean-value Theorems[J].Journal of Foshan University(Natural Science Edition),2006,24(3):8-10. |
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| Authors: | TAN Yue-hua XIE Chun-e |
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| Institution: | 1. Foshan Senior Technical School, Foshan 528000, China; 2. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China |
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| Abstract: | The relations in differential mean-value theorems are studied based on geometrical meaning and global point of view in this paper.The different forms of Rolle Theorem,Lagrange Theorem and Cauchy Theorem unified in differential mean-value theorems are also discussed.With Rolle Mean-value Theorem and different assisting functions,some other diversified forms of differential mean-value theorems can be demonstrated. |
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| Keywords: | differential mean-value theorems relations unified assisting functions |
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