Applications of Differentiation
2007-05-15 9:08 am
If the curve , where k<>0(not equal to 0), has no stationary points, find the range of values of k.
回答 (1)
2007-05-15 10:47 am
✔ 最佳答案
y=f(x)=kx^3+3x^2+(k-2)x+1if no stationary points, then f'(x) should not be equal to 0
f'(x)=3kx^2+6x+(k-2)
Since f'(x) <> 0
The discriminant should be less than 0
So
6^2-4(3k)(k-2)<0
36-12k(k-2)<0
3-k(k-2)<0
3-k^2+2k<0
k^2-2k-3>0
(k-3)(k+1)>0
k<-1 or k>3
The range of values of k is k<-1 or k>3
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