题目
题型:东营一模难度:来源:
2 |
3 |
(1)求a,b的值;
(2)若f(-1)=
3 |
2 |
(3)若对x∈[-1,2]都有f(x)<
3 |
c |
答案
由题设,∵函数f(x)=x3+ax2+bx+c在x=1与x=-
2 |
3 |
∴x=1,x=-
2 |
3 |
∴-
2 |
3 |
2 |
3 |
b |
3 |
2 |
3 |
解得a=-
1 |
2 |
此时,f′(x)=3x2-x-2=(x-1)(x+
2 |
3 |
2 |
3 |
(2)f (x)=x3-
1 |
2 |
1 |
2 |
3 |
2 |
∴f (x)=x3-
1 |
2 |
2 |
3 |
3 |
2 |
3 |
c |
2 |
3 |
2 |
3 |
2 |
3 |
2 |
3 |
b |
3 |
2 |
3 |
1 |
2 |
2 |
3 |
2 |
3 |
1 |
2 |
1 |
2 |
3 |
2 |
1 |
2 |