Consider the following function and closed interval.

$f(x)=(x-2)(x-4)(x-7),[2,7]$

Is $f$ continuous on the closed interval $[2,7]?$

Yes

No

If $f$ is differentiable on the open interval $(2,7),$ find $f^{\text{'}}(x).($If it is not differentiable on the open interval, enter DNE.$)$

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

Find $f(2)$ and $f(7).$

$f(2)=$

$f(7)=$

Determine whether Rolle's Theorem can be applied to $f$ on the closed interval $a,b.($Select all that apply.$)$

Yes, Rolle's Theorem can be applied.

No$,$ because $f$ is not continuous on the closed interval $a,b.$

No$,$ because $f$ is not differentiable in the open interval $(a,b).$

No$,$ because $f(a)f(b).$

If Rolle's Theorem can be applied, find all values of $c$ in the open interval $(a,b)$ such that $f^{\text{'}}(c)=0.($Enter your answers as a comma$-$separated list. If Rolle's Theorem cannot be applied, enter NA$.)$

$c=$