A) \[k<3\]
B) \[k\le 3\]
C) \[k>3\]
D) \[k\ge 3\]
Correct Answer: C
Solution :
[c] Given \[f(x)=k{{x}^{3}}-9{{x}^{2}}+9x+3\] On differentiating w.r.t.x, we get \[f'(x)=3k{{x}^{2}}-18x+9\] For a function to be monotonically increasing. \[{{b}^{2}}-4ac<0\] Here, \[a=3k,b=-18,c=9\] \[\therefore {{b}^{2}}-4ac={{(-18)}^{2}}-4(3k)(9)\] \[=(-18)(-18)-(3k)18\times 2\] \[\Rightarrow 36-12k<0\Rightarrow k>3\]You need to login to perform this action.
You will be redirected in
3 sec