Question

Function $f\left(x\right)=x^3-3x^2-9x+20$ is monotonic increasing when-

• A. $x>-1$
• B. $x>3$ or $x<-1$
• C. $-1<x<3$
• D. $x<-1$

Answer 1

The correct option is B $x>3$ or $x<-1$

Given, $f\left(x\right)=x^3-3x^2-9x+20$

$f^{\prime }\left(x\right)>0$
Hence, $3x^2-6x-9>0$
$\Rightarrow 3(x^2-2x-3)>0$
$\Rightarrow 3(x-3)(x+1)>0$
$\Rightarrow x>3$ and $x<-1$