Question

设f(x)在x=0处连续,且lim(x趋于0）f(x)/x^2=1 ,证明函数f(x)在x=0处可导且取得极小值.

Answer 1

1、f(0)＝lim f(x)＝lim f(x)/x^2 *lim x^2＝1*0＝0,

于是f'(0)＝lim [f(x)－f(0)]/x

=lim f(x)/x^2*x

＝lim f(x)/x^2 *lim x

=1*0＝0,

即f'(0)=0.

2、对e＝1/2,存在d>0,使得

0