Given $f(x)=x+\frac{36}{x}.$

$($a$)$ Find the intervals on which $f$ is increasing or decreasing.

$($b$)$ Find the relative maxima and relative minima of $f.$

$($a$)$ Increasing on $(-,-6)$ and $(6,),$ decreasing on $(-6,6)$

$($b$)$ Rel. max. $f(-6)=-12,$ rel. min. $f(6)=12$

$($a$)$ Increasing on $(-6,0)$ and $(0,6)$ decreasing on $(-,-6)$ and $(6,)$

$($b$)$ Rel. max. $f(6)=12,$ rel. min.$f(-6)=-12$

$($a$)$ Increasing on $(-,-6)$ and $(6,),$ decreasing on $(-6,0)$ and $(0,6)$

$($b$)$ Rel. max. $f(-6)=-12,$ rel. min. $f(6)=12$

$($a$)$ Increasing on $(-6,6),$ decreasing on $6$ and $(6,)$

$($b$)$ Rel. max. $f(6)=12,$ rel. min.$f(-6)=-12$