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 $(-2,0)$ and in $(0,1)$
• D. decreasing in $(-\infty,-2)$ and in $(1, \infty)$

Answer 1

Answer: (B)

$\because f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12 f(x)=12 x^{3}+12 x^{2}-24 x$
$=12 x\left(x^{2}+x-2\right)$
$=12 x(x-1)(x+2)$
From above it is clear that $f(x)$ is increasing in $(-2,0)$ and in $(1, \infty)$