A) \[(-\infty ,-1)\cap (3,\,\infty )\]
B) \[(1,\,\,3)\]
C) \[(3,\,\,\infty )\]
D) None of these
Correct Answer: B
Solution :
\[f(x)={{x}^{3}}-6{{x}^{2}}+9x+3\], For decreasing \[{f}'(x)<0\] Þ \[3{{x}^{2}}-12x+9<0\] Þ \[{{x}^{2}}-4x+3<0\] Þ \[(x-3)\,\,(x-1)<0\], \ \[x\in (1,\,3)\].
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