A) \[(2,3)\]
B) \[(1,2)\]
C) \[(-2,1)\]
D) \[(-3,-2)\]
Correct Answer: C
Solution :
Given, \[f(x)=2{{x}^{3}}+3{{x}^{2}}-12x+1\] \[\Rightarrow \] \[f'(x)=6{{x}^{2}}+6x-12\] For \[f(x)\] to be decreasing, \[f'(x)<0\] \[\Rightarrow \] \[6{{x}^{2}}+6x-12<0\] \[\Rightarrow \] \[{{x}^{2}}+x-2<0\] \[\Rightarrow \] \[(x+2)(x-1)<0\] \[\Rightarrow \] \[x\in (-2,1)\]You need to login to perform this action.
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