Question

If $ f(x)=3{{x}^{4}}+4{{x}^{3}}-12{{x}^{2}}+12, $ then $ f(x) $ is

• 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 $(0,1)$

Answer 1

Answer: (B)

$ \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 ) $