摘 要:微分中值定理作为微分学中的重要定理和核心理论,是微分学应用的理论基础,在数学分析中发挥了重要的作用.本毕业论文首先简述了罗尔定理、拉格朗日中值定理和柯西中值定理产生的历史背景,其次研究了罗尔定理、拉格朗日中值定理和柯西中值定理的多种证明方法,最后给出了各个定理的应用实例,从而加深了对微分中值定理的理解与掌握.7421
关键词:罗尔定理;拉格朗日中值定理;柯西中值定理
The provation and the application of the differential mean value theorem
Abstract: The differential mean value theorem, as the important and the core theorem of the differential,is the theoretical basis of the application of differential. It plays an important role in mathematical analysis. This paper describes the historical background of the Rolle mean value theorem、Lagrange mean value theorem and Cauchy mean value theorem firstly.Then gives a variety methods of the provation of them. Lastly, the paper introduces some examples of the application of the theorems. So that people can get deeply understanding.
Key words: Rolle mean value theorem;Lagrange mean value theorem;Cauchy mean value theorem;The structure method of auxiliary function
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