Question

$f\left(x\right)=x^3-27x+5$ is monotonically increasing for

• A. $x<-3$
• B. $|x|>3$
• C. $|x|<3$
• D. $x>3$

Answer 1

The correct option is B $|x|>3$

$f^{\prime }\left(x\right)=3x^2-27$
$=3(x^2-9)$
monotonically increasing $\Rightarrow f^{\prime }\left(x\right)>0$ $\Rightarrow 3(x^2-9)>0\Rightarrow \mid x\mid >3$
monotonically decreasing $\Rightarrow f^{\prime }\left(x\right)<0$ If $\mid x\mid <3$