Consider the following function and closed interval.

SCalaty $4\mathrm{.}2$ pror

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

Is $f$ continuous on the closed interval $-4,4?$

Yes

No

If $f$ is differentiable on the open interval $(-4,4),$ find $f^{\text{'}}(x).($If it is not differentiable on the open interval, enter Dive.$)$

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

$$

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

$(f-4)=$

$$

$f(4)=$

$$

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

Yes, Rolle's Theorem can be applied.

No$,$ because $f$ is not continuous on the closed interval $\{-4,4\}.$

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

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

e $-$