| 微分学中值定理的证明及其在应用中应注意的问题 |
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| 引用本文： | 关金玉,祁建芳,董玉龙.微分学中值定理的证明及其在应用中应注意的问题[J].河北北方学院学报(自然科学版),2005,21(5):14-15,19. |
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| 作者姓名： | 关金玉 祁建芳 董玉龙 |
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| 作者单位： | 河北北方学院数学系,河北,张家口,075000;河北北方学院数学系,河北,张家口,075000;河北北方学院数学系,河北,张家口,075000 |
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| 摘 要： | 通过构造辅助函数简化了微分中值定理的证明，并通过构造2个例子指出应用微分中值定理时应注意的问题：（1）定理只指出了中间值的存在，并未具体给出求中间值的方法；（2）中间值既依赖于函数本身，且与端点a、b有关。它们之间的依赖关系是相当复杂的；（3）当区间端点连续变化时，相应的中间值并不一定连续变化．
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| 关 键 词： | 中值定理 辅助函数 中间值 |
| 文章编号： | 1673-1492（2005）05-0014-02 |
| 收稿时间： | 09 5 2005 12:00AM |
| 修稿时间： | 2005-09-05 |
The Proof of Mean Value Theorem and Noticeable Questions in Application |
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| GUAN Jin-yu,QI Jian-fang,DONG Yu-long.The Proof of Mean Value Theorem and Noticeable Questions in Application[J].Journa of Hebei North University:Natural Science Edition,2005,21(5):14-15,19. |
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| Authors: | GUAN Jin-yu QI Jian-fang DONG Yu-long |
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| Institution: | Department of Mathematics, Hebei North University, Zhangjiakou, Hebei 075000, China |
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| Abstract: | To simplify the prove process of Mean Value Theorem by constructing a accessorial function, and puts forward some noticeable questions in application by constructing two examples. First, it is pointed out in Mean Value Theorem that the mid--value exists, but it is not metioned how to seek after the mid-value. Second, the mid--value relates to not only the function itself but also the endpoints a and b. Third, it is not certain that the mid--value varies continuously while the endpoints vary continuously. |
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| Keywords: | mid-value theorem accessorial function mid-value |
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