Question

设f(x)可导,F（x）=f(x)(1+|sinx|),若F（X）在点x=0处可...

设f(x)可导,F（x）=f(x)(1+|sinx|),若F（X）在点x=0处可导,则必有（?） A,f(0)=0 B,f'(0)=0 C,f(0)+f'(0)=0 D,f(0)-f'(0)=0 谢谢各位了,把过程也写清楚点我追加分!

Answer 1

选A，详情如图所示

Answer 2

在0附近xo时F(x)=f(x)(1+sinx)x0时F'(x)=f'(x)+f'(x)sinx+f(x)sin'x
[2]因为F(x)在
x=0处可导所以
x趋向于0-时于趋向于0+时
F'(0)-
=
F'(0)+所以X=0时
【1】式=【2】式所以f'(0)-f'(0)sin0-f(0)sin'0
=f'(0)+f'(0)sin0+f(0)sin'0
整理
知f(0)=0选A