$4\mathrm{.}3$ #$11.$a$.$ Find the local extrema of the function $f(x)=\sqrt[\phantom{2}]{3}cos5x+sin5x$ on the interval $0x\frac{2}{5},$ and say where they occur.

b$.$ Graph the function and its derivative together. Comment on the behavior of $f$ in relation to the signs and values of $f^{\text{'}}.$

a$.$ Find each local maxima, if there are any. Select the correct choice below and fill in any answer boxes within your choice. $($Simplify your answers. Type exact answers, using $$ as needed. Use integers or fractions for any numbers in the expression.$)$

A$.$ The function has a local maximum at one value of $x.$ The maximum value is $=$

$7.$

B$.$ The function has a local maximum value at two values of $x.$ In increasing order of $x-$value, the maximum values are $f=$ and f $(=$

C$.$ The function has a local maximum value at three values of $x.$ In increasing order of $x-$value, the maximum values are $f=,1=$ and f

D$.$ There are no local maxima.