Question

已知f(x)=x^3+(k-1)x^2+(k+5)x-1在区间(0,3)上不单调，求K取值范围，求思路解释啊

Answer 1

解：f'(x)=3x^2+2(k-1)x+k+5
由f(x)=x^3+(k-1)x^2+(k+5)x-1在区间(0,3)上不单调，则f'(x)=0在区间(0,3)上有解.
即f'(0)f'(3)≤0
(k+5)(7k+26)≤0
-5≤k≤-26/7
K取值范围[-5,-26/7]

Answer 2

f'(x) = 3x^2+2(k-1)x+(k+5)
∵f(x)在区间（0,3）上不单调
∴f'(0) * f'(3) < 0
(k+5)(k+5+6k-6+27) < 0
(k+5)(7k+26)<0
- 5 < k < -26/7

追问

为什么答案是(-5,-2)呢

追答

答案错了呗！！！

Answer 3

答案的确是(-2,-5)如果你需要过程我就打给你？