Consider the following function and closed interval.

$f(x)=x^3-4x^2-16x+2,[-4,4]$

$Isf$ continuous $on$ the closed interval $-4,4?$

Yes

$No$

$Iffis$ differentiable $on$ the open interval $(-4,4),$ find $f^{\text{'}}(x).(Ifitis$ not differentiable $on$ the open interval, enter DNE.$)$

$f^{\text{'}}(x)=$

Find $f(-4)$ and $f(4).(Ifan$ answer does not exist, enter DNE.$)$

$f(-4)=$

$f(4)=$

Determine whether Rolle's theorem can $be$ applied $tofon$ the closed interval $-4,4.(Select$ all that apply.$)$

Yes, Rolle's Theorem can $be$ applied.

$No,$ because $fis$ not continuous $on$ the closed interval $-4,4.$

$No,$ because $fis$ not differentiable $on$ the open interval $(-4,4).$

$No,$ because $f(-4)f(4).$

$c=$