Consider the following given function and given interval.

$f(x)=6sin(x)-3sin(2x),[0,]$

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

$f_{\text{a}\text{v}\text{e}}=10$

$($b$)$ Find $c$ in the given interval such that $f_{\text{a}\text{v}\text{e}}=f(c).($Enter your answers as a comma$-$separated list. Round your answers to three decimal places.$)$

$c$

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