| 1 |
| 3 |
∴f′(x)=x2-4=(x+2)(x-2),
令f′(x)=0,解得x=-2,或x=2,
列表讨论,得:
| x | (-∞,-2) | -2 | (-2,2) | 2 | (2,+∞) |
| f′(x) | + | 0 | - | 0 | + |
| f(x) | ↑ | 极大值 | ↓ | 极小值 | ↑ |
∵函数f(x)=
| 1 |
| 3 |
| 28 |
| 3 |
∴f(-2)=
| 8 |
| 3 |
| 28 |
| 3 |
解得m=4.
(2)由m=4,得f(x)=
| 1 |
| 3 |
当x=2时,f(x)取极小值f(2)=-
| 4 |
| 3 |
| 1 |
| 3 |
| 28 |
| 3 |
| 1 |
| 3 |
| x | (-∞,-2) | -2 | (-2,2) | 2 | (2,+∞) |
| f′(x) | + | 0 | - | 0 | + |
| f(x) | ↑ | 极大值 | ↓ | 极小值 | ↑ |
| 1 |
| 3 |
| 28 |
| 3 |
| 8 |
| 3 |
| 28 |
| 3 |
| 1 |
| 3 |
| 4 |
| 3 |