利用微分学理论证明不等式的常用方法

Common Methods Using Differential Theory to Prove Inequality

不等式的证明是《高等数学》课程的重要内容之一.为了帮助学员更熟练地掌握利用微分学理论证明不等式的方法,本文就利用微分学理论证明不等式的常用方法进行总结,提出可以利用函数的单调性、利用拉格朗日中值定理和利用泰勒公式三种方法来证明不等式.

The proof of inequality is one of the important contents of Higher Mathematics course. In order to help the students grasp the methods of the in differential knowledge are researched in this monotonicity, Lagrange mean-value theorem equality＇ s proof by using differential theory, the common methods using paper. Furthermore, three approaches are discussed that include using and Taylor formula.