Consider the given function and the given interval.

$f(x)=2\sqrt[\phantom{2}]{x},[0,25]$

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

$f_{\text{a}\text{v}\text{e}}=6\mathrm{.}67$

$($b$)$ Find c such that $f_{\text{a}\text{v}\text{e}}=f(c).($Round your answer to ofree decimal places.$)$

$c=$

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