Mathematics - Application of Derivative Question with Solution | TestHub

$f\left(x\right)=\left\{\begin{array}{ll}-55x,& \mathrm{if} x<-5\\ 2x^3-3x^2-120x,& \mathrm{if}-5\le x\le 4\\ 2x^3-3x^2-36x-336,& \mathrm{if} x>4\end{array}\right.$

$f\text{'}\left(x\right)=\left\{\begin{array}{ll}-55,& \mathrm{if} x<-5\\ 6x^2-6x-120,& \mathrm{if}-5\le x\le 4\\ 6x^2-6x-36,& \mathrm{if} x>4\end{array}\right.$

$f^{\text{'}}\left(x\right)=\left\{\begin{array}{cc}-55;& x<-5\\ 6\left(x-5\right)\left(x+4\right);& -5<x<4\\ 6\left(x-3\right)\left(x+2\right);& x>4\end{array}\right.$

$f\left(x\right)$ is increasing

$\Rightarrow f^{\text{'}}\left(x\right)>0$

So, $x\in \left(-5,-4\right)\cup \left(4,\infty \right)$