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 |