关于曲线凹凸性的两个定理及应用

The Application of Two Theories Related to the Properties of Concave and Convex Function

历年考研题目中经常出现有关不等式证明的题目,很多证明都要使用拉格朗日中值定理以利用导数来判断函数的特性;另一方面我们可以用凹凸性(即二阶导数)确定导函数增减的一些性质,将两者结合得到了在凹凸性已知的前提下中值定理的进一步的结论。根据这个结论,在解题时可以利用画图等手段帮助寻找满足条件的函数与区间,简化证明过程,并得到最终需要的结论。

Many inequality questions appeared in the postgraduate entrance examination in recent years.Some related results on Lagrange＇s mean value theorem combined with the properties of concave and convex functions are obtained,which could help to find the suitable function and interval,simplify the process of proving,and get the conclusion finally.