Applications Of Derivatives Question 72
Question: If $ f(x)=kx^{3}-9x^{2}+9x+3 $ is monotonically increasing in each interval, then
[RPET 1992; Kurukshetra CEE 2002]
Options:
A) $ k<3 $
B) $ k\le 3 $
C) $ k>3 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f’(x)=3kx^{2}-18x+9=3[kx^{2}-6x+3]>0,\forall x\in R $
$ \therefore \Delta =b^{2}-4ac<0,,k>0 $
$ i.e.,\ \ 36-12k<0 $ or $ k>3 $ .
BETA
