关于极值第一判别法的一个注记

A Remark About the First_Derivative Test of Relative Extrema

若ｆ′（ｘ）在ｘ０两侧符号不相同，则ｆ（ｘ０）是极值；若ｆ′（ｘ）在ｘ０两侧符号相同，则ｆ（ｘ０）不是极值。本文指出了常被忽略的第三种情况，即ｆ′（ｘ）在ｘ０两侧有不确定的符号，此时ｆ（ｘ０）可能是也可能不是极值，文中给出了两个例子。

If f′(x) has different sign to the left and right of x 0 ,then f(x 0) is a relative extremum.If f′(x 0) has the same sign on both sides of x 0 ,then f(x 0) is not a relative extremum.We point out the third situation wihich is often neglected,that is, f′(x) has indefinite sign on both sides of x 0 .In this case f(x 0) may or may not be a relative extremum.Two examples are given in this paper.