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)

increasing in $(-2,0)$ and in $(1, \infty)$

Answer 2

The correct option is (B): increasing in (−2,0) and in (1,∞).
$f(x)=3 x^{4}+4 x^{3}-12 x^{2}+12$
$f(x)=12 x^{3}+12 x^{2}-24 x$
$=12 x(x-1)(x+2)$
By putting f'(x)=0 we get x=-2, 0, 1.
From above it is clear that f(x) is increasing in (-2,0) and in $(1, \infty)$