Applications Of Derivatives Question 79
Question: For which interval the given function $ f(x)=-2x^{3}-9x^{2}-12x+1 $ is decreasing
[MP PET 1993]
Options:
A) $ (-2,,\infty ) $
B) $ (-2,,-1) $
C) $ (-\infty ,,-1) $
D) $ (-\infty ,-2) $ and $ (-1,,\infty ) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=-2x^{3}-9x^{2}-12x+1 $
therefore $ f’(x)=-6x^{2}-18x-12 $ To be decreasing $ f’(x)<0 $ , i.e., $ -6x^{2}-18x-12<0 $
therefore $ x^{2}+3x+2>0 $
therefore $ (x+2)(x+1)>0 $
Therefore either $ x<-2 $ or $ x>-1 $
therefore $ x\in (-1,\infty ) $ or $ (-\infty ,-2) $ .
BETA
