## 函数的凹凸性在不等式证明中的应用

1.预备知识    3
1.1 凹凸函数的定义    3
1.2 凹凸函数的图形特征    3
1.3 凹凸函数的性质、定理    4
2.函数的凹凸性在证明不等式的应用    5
2.1函数凹凸性在经典不等式中的应用    5
2.2 初等函数凹凸性在不等式证明中的应用    10
2.3函数的凹凸性在证不等式中数形结合的应用    14
3.结束语    15

The Application of Concave Convex Functionsin anInequation
Abstract:Proof of Function irregularities inequality is an essential element of inequality is an important method to prove convexity functions is the mathematical analysis. In this paper, the definition of sexual function irregularities, as well as the nature of theorems, to take advantage of the function of some of the classic irregularities Elementary inequality and inequality to prove inequality and select appropriate examples summarize how the irregularities of the function to prove inequality general methods and ideas, and to further explore the proof of inequality and uneven application of the constructor function inequality.

Keywords:Function of concave and convex; Inequality proof; Application

1.预备知识
1.1凹凸函数的定义

（1）

(2)

，  (4)

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