利用导数的因子判断极值点和拐点

Judgmentof extreme point and inflexion point through factors

本文通过研究从导数f′ (x) (或f″ (x) )中分解出来的一些因子在其零点左右两侧的符号变化情况 ,寻找出这些零点与极值点 (或拐点 )之间的必然联系 ,并以此为基础 。

The present paper argues the changes of the factors from f(x)in either the right or left side of zero point, in the hope of finding out the inevitable relation between zero point and extremepoint (inflexion point). The author also discusses the extreme point and the inflexion point of polynomial function and rational function.