Question

If $f\left(x\right)=3x^4+4x^3-12x^2+12$, then $f\left(x\right)$ 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

The correct option is B

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

Explanation for the correct option.

$f\left(x\right)=3x^4+4x^3-12x^2+12$

Differentiating with respect to $x$, we get

$\begin{array}{rcl}f\text{'}\left(x\right)& =& 12x^3+12x^2-24x\\ & =& 12x\left(x^2+x-2\right)\\ & =& 12x\left(x-1\right)\left(x+2\right)\end{array}$

Now, by putting $f\text{'}\left(x\right)=0$, we get $x=-2,0,1$.

This shows that $f\left(x\right)$ is increasing in $(-2,0)$ and in $(1,\infty )$.

Hence, option B is correct.