f'+(1)=
lim |
x→0+ |
f(1+x)−f(1) |
x |
lim |
x→0+ |
af(x)−af(0) |
x |
f'-(1)=
lim |
x→0− |
f(1+x)−f(1) |
x |
lim |
x→0− |
af(x)−af(0) |
x |
所以,f'+(1)=f'-(1)=ab
所以,f(x)在x=1处可导,且f′(1)=ab
故选:D.
lim |
x→0+ |
f(1+x)−f(1) |
x |
lim |
x→0+ |
af(x)−af(0) |
x |
lim |
x→0− |
f(1+x)−f(1) |
x |
lim |
x→0− |
af(x)−af(0) |
x |