A) \[(-2,\,\infty )\]
B) \[(-2,\,-1)\]
C) \[(-\infty ,\,-1)\]
D) \[(-\infty ,\,\,-2)\]and \[(-1,\,\infty )\]
Correct Answer: D
Solution :
\[f(x)=-2{{x}^{3}}-9{{x}^{2}}-12x+1\]Þ\[f'(x)=-6{{x}^{2}}-18x-12\] To be decreasing \[f'(x)<0\], i.e.,\[-6{{x}^{2}}-18x-12<0\] Þ\[{{x}^{2}}+3x+2>0\]Þ\[(x+2)(x+1)>0\] Therefore either \[x<-2\] or \[x>-1\] Þ\[x\in (-1,\infty )\] or \[(-\infty ,-2)\].
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