Question

For which interval, the given function $ f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1 $ is decreasing?

• A. $ (-2,\,\,\infty ) $
• B. $ (-2,\,\,-1) $
• C. $ (-\infty ,\,\,-1) $
• D. $ (-\infty ,\,\,-2) $ and $ (-1,\,\,\infty ) $

Answer 1

Answer: (D)

Given, $ f(x)=2{{x}^{3}}-9{{x}^{2}}-12x+1 $
$ \Rightarrow $ $ f'(x)=-6{{x}^{2}}-18x-12 $
To be decreasing, $ f'(x)<0 $
$ \Rightarrow $ $ -6{{x}^{2}}-18x-12<0 $
$ \Rightarrow $ $ {{x}^{2}}+3x+2>0 $
$ \Rightarrow $ $ (x+2)(x+1)>0 $
$ \therefore $ Either $ x<-2 $ or $ x>-1 $
$ \Rightarrow $ $ x\in (-1,\,\,\infty ) $ or $ (-\infty ,\,\,-2) $