Find the $absolute$ maximum and $absolute$ minimum values $offon$ the given interval.

$f(x)=6x^3-9x^2-108x+6,[-3,4]$

Step $1$

The $absolute$ maximum and minimum values $off$ occur either $at$ a critical point inside the interval $oratan$

endpoint $of$ the interval. Recall that a critical point $is$ a point where $f^{\text{'}}(x)=0oris$ undefined. $We$ begin $by$ finding

the derivative $off.$

$f^{\text{'}}(x)=18x^2-18x-108$

Step $2$

$We$ now solve $f^{\text{'}}(x)=0$ for $x,$ which gives the following critical numbers. $(Enter$ your answers $as$ a comma$-$

separated list.$)$

$x=$

Step $3$

$We$ must now find the function values $at$ the critical numbers $we$ just found and $at$ the endpoints $of$ the interval

$-3,4.$

$f(-2)=$

$f(3)=$

$f(-3)=$

$f(4)=$