Find the critical points and the interval on which the

given function is increasing or decreasing, and apply the

First Derivative Test to each critical point. Let

$f(x)=\frac{2}{4}{x}^4+\frac{6}{3}{x}^3+\frac{-8}{2}{x}^2-24x$

There are three critical points. If we call them $c_1,c_2,$ and

$c_3,$ with $c_1=c_2=c_3=f{c}_1,f{c}_2,f{c}_3,ff{f}^{\text{'}}f{f}^{\text{'}}f{f}^{\text{'}}f{f}^{\text{'}}{c}_1,$ then

$c_1=$

$c_2=$

and $c_3=$

$Isf$ a maximum $or$ minumum $at$ the critical points?

$At{c}_1,fis$

$At{c}_2,fis$

$At{c}_3,fis$

These three critical give $us$ four intervals.

The left$-$most interval $is$

$,$ and $on$

this interval $fis$

while $f^{\text{'}}is$

The next interval $(going$ left $to$ right$)is$

$.On$ this interval $fis$

while $f^{\text{'}}is$

Next $is$ the interva

$.On$ this

interval $fis$

while $f^{\text{'}}is$

Finally, the right$-$most interval $is$

$On$ this interval $fis$

while $f^{\text{'}}is$