Question

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

• A. increasing in $\left(- \infty , - 2\right)\cup\left(0 , \, 1\right)$
• B. increasing in $\left(- 2 , 0\right)\cup\left(1 , \infty \right)$
• C. decreasing in $\left(- 2 , 0\right)\cup\left(0 , 1\right)$
• D. decreasing in $\left(- \infty , \, - 2\right)\cup\left(1 , \, \infty \right)$

Answer 1

Answer: (B)

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