拉格朗日中值定理证明及其应用

来源:用户上传      作者:李兵方

　　摘要：拉格朗日中值定理是微分學突出的成果，在微积分中占有非常重要的地位，且它是微分学的基础定理之一，是沟通函数与导数之间的桥梁，在理论及其应用上都有极其重要的意义。通过对定理的再认识，对拉格朗日中值定理的应用做了一定研究，主要探讨了拉格朗日中值定理在求极限、证明不等式、证明函数单调性等方面的应用。
　　关键词：拉格朗日定理;罗尔定理;应用
　　中图分类号：O171     文献标志码：A     文章编号：1674-9324（2020）14-0294-02
　　Abstract：Lagrange theorem is differential prominent achievements in the mathematical analysis plays a very important position，and it is the basis of theorem of differential calculus is one of communication between function and derivative of the bridge，in the theory and its applications all have very important meaning.Recognition by theorem of Lagrange's theorem to do an analysis，on the application of Lagrange theorem to do a little research，a comprehensive understanding of the Lagrange mean value theorem in limit，to prove inequality，that function monotonicity aspects of role to play on the theorem in-depth understanding and mastery of the role can be applied correctly.
　　Key words：Lagrange;Rolle theorem;application
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