Question

The function $f\left(x\right)=x^3-3x^2+6$ is an increasing function for:

• A. $0<x<2$
• B. $x<2$
• C. $x>2$ or $x<0$
• D. all $x$

Answer 1

The correct option is C $x>2$ or $x<0$

$f\left(x\right)=x^3-3x^2+6$

Differentiating, we get

$f^{\prime }\left(x\right)=3x^2-6x$
A function is increasing when it's derivative is $>0$
So, for given function
$3x^2-6x>0\Rightarrow 3x(x-2)>0$

$\Rightarrow x>2$ or $x<0$
Option C is true