Question

If $f(x)=3x^4+4x^3-12x^2+12$, 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)

Given : $f\left(x\right)=3x^4+4x^3-12x^2+12$
Differentiating with respect to x, we get
$f^{\prime }\left(x\right)=12x^3+12x^2-24x$
For f (x) to be increasing
f '(x) > 0
$\Rightarrow 12x^3+12x^2-24x>0$
$\Rightarrow 12x(x^2+x-2)>0$
$\Rightarrow 12x(x-1)(x+2)>0$
$\Rightarrow x(x-1)(x+2)>0$
$\Rightarrow -2<x<0$ or $x>1$