A) \[(-\infty ,-3)\]
B) \[(2,\infty )\]
C) \[(-3,2)\]
D) \[(-\infty ,-3)\cup (2,\infty )\]
Correct Answer: C
Solution :
\[f(x)=\frac{1}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}}-6x+8\] On differentiating w.r.t.\[x,\] \[f'(x)={{x}^{2}}+x-6\] Since,\[f(x)\]is decreasing \[\therefore \] \[f'(x)<0\] \[\Rightarrow \] \[{{x}^{2}}+x-6<0\] \[\Rightarrow \] \[(x+3)(x-2)<0\] \[\Rightarrow \] \[x<2,x>-3\] Hence, required interval is\[(-3,2)\].
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