Applications Of Derivatives Question 86
Question: In which interval is the given function $ f(x)=2x^{3}-15x^{2}+36x+1 $ is monotonically decreasing
[RPET 1995]
Options:
A) [2, 3]
B) (2, 3)
C) $ (-\infty ,,2) $
D) $ (3,,\infty ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=f(x)=2x^{3}-15x^{2}+36x+1 $
$ \frac{dy}{dx}=f’(x)=6x^{2}-30x+36=6(x^{2}-5x+6) $
$ f’(x)=6(x-2)(x-3) $ To be monotonic decreasing, $ f’(x)<0 $
$ \Rightarrow (x-2)(x-3)<0\Rightarrow x\in (2,3) $ .
BETA
