Question

若函数f(x)=e的ax次方x0,处处可导,则a和b的值为多少

Answer 1

f(x)=e^(ax) x0
处处可导,这x=0时连续,即:f(0+)=f(0-)
f(0+)=b(1-0)=b
f(0-)=e^(a*0)=1
所以:b=1
又:可导,则f'(0+)=f'(0-)
f'(x)=ae^(ax) x