A) \[(-2,\,\,\infty )\]
B) \[(-2,\,\,-1)\]
C) \[(-\infty ,\,\,-1)\]
D) \[(-\infty ,\,\,-2)\]and\[(-1,\,\,\infty )\]
Correct Answer: D
Solution :
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\[(-\infty ,\,\,-2)\]
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