Consider the following function and interval.

$f(x)=(x-3{)}^2,[2,5]$

$($a$)$ Find the average value $f_{\text{a}\text{v}\text{e}}$ of $f$ on the given interval.

$f_{\text{a}\text{v}\text{e}}=$

$($b$)$ Find all values of $c$ such that $r_{\text{a}\text{v}\text{e}}=f(c).($Enter your answers as a comma$-$separated list.$)$

$c=$

$($c$)$ Sketch the graph of $f$ and a rectangle whose area is the same as the ares under the oranh of $f.$