Question

If $f\left(x\right)=3x^4+4x^3-12x^2+12$ , then $f(x)$ 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, $f(x)=3x^4+4x^3-12x^2+12$
$f^{{}^{\prime }}\left(x\right)=12x^3+12x^2-24x$
$=12x\left(x-1\right)(x+2)$
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 $\left(-\infty ,-2\right)\cup \left(0,1\right)$