微分中值定理的探讨与应用.doc

摘要:　微分中值定理是沟通导数和函数之间的桥梁，应用十分广泛。本文主要介绍常用的微分中值定理，罗尔定理，拉格朗日定理，柯西定理以及之间的内在联系，推广及在解题中的应用，利用微分中值定理讨论导函数零点的存在性，证明不等式及等式，研究函数的性态及求极限，从而加深对微分中值定理的理解。

关键词：罗尔定理 ；拉格朗日定理； 柯西定理；导数

Abstract:　Differential intermediate value theorem is communication between the derivative and functions of bridges and widely applied .The paper introduces rolle theorem ,lagrange theorem, cauchy theorem, elaborates theorem ,elaborates the relationship between differential value theorems , popularity and  application in solving problems .Disscusses application of differential intermediate value theorems, such as proving existence of roots of equation ,proving equality and inequality ,study properties of functions, seeking extreme value. This deepens one’s comprehension for differential intermediate value theorem.

Key words: Rolle Theorem ; Lagranian Theorem; Cauchy Theorem; Derivative

　微分中值定理是微分学的基本定理，在数学分析中占有重要地位，是研究函数在某个区间的整体性质的有利工具。它包括罗尔定理、拉格朗日中值定理和柯西中值定理，它架起了沟通函数与导数之间的桥梁，应用十分广泛。本文将讨论微分中值定理的内在联系、推广，并阐述它的若干应用。