利用插值余项证明含导数的一类不等式

An Inequality with derivative proved by Interpolation Remainder Term

利用拉格朗日插值及余项构造辅助函数用于证明含导数的一类不等式,得到了一种有效方法,称之为插值解法。与"利用泰勒公式证明该类不等式"的常规做法相比较,插值解法更简洁、易懂且有规律可循,能起到事半功倍的效果。

This paper uses Lagrangian interpolation and co-term constructor functions to prove a class of inequalities containing derivatives.We called it interpolation method.Compared with the conventional approach by using the Taylor’s formula to prove the inequalities,this method is not only more concise and easy to understand.It can also provide some rule to follow and play a multiplier effect.