A) increasing in\[(-\infty ,-2)\]and in (0, 1)
B) increasing in\[(-2,0)\] and in\[(1,\infty )\]
C) decreasing in\[(-2,\text{ }0)\]and in (0, 1)
D) decreasing in\[(-\infty ,-2)\] and in\[(1,\text{ }\infty )\]
E) increasing in\[(-2,\text{ }0)\]and in (0,1)
Correct Answer: B
Solution :
\[\because \]\[f(x)=3{{x}^{4}}+4{{x}^{3}}-12{{x}^{2}}+12\] \[f(x)=12{{x}^{3}}+12{{x}^{2}}-24x\] \[=12x({{x}^{2}}+x-2)\] \[=12x(x-1)(x+2)\] From above it is clear that \[f(x)\]is increasing in\[(-2,0)\]and in\[(1,\infty )\]
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