一元绝对值函数可导性的讨论

Discussion on Derivative of AbsoluteValue Function of One Variable

文章讨论了一元绝对值函数的可导性。文中首先推广了一个一般性的结论:函数f(x)=|x|在x=0处不可导,指出当α>0时f(x)=xα|x|在x=0处可导,并进一步推广了该结论。接着讨论了当f(x)在x=x0处可导时,|(fx)|在x=x0处的可导性。最后给出了两个具体的例子。

It discusses the derivative of absolute value functions with one variable.Firstly,a general conclusion is promoted,that is,the function f（x）=｜x｜ does not exist derivation at x=0,but if α0,f（x）=xα｜x｜ exists derivation at x=0,and we get an another conclusion.Then it discusses the derivative of function ｜f（x）｜ at x=x0 if f（x） gets derivation there.In the end of this paper,two examples are showed.