a. Find the local extrema of the function $f(x) = \frac{x}{2} - 4\sin\frac{x}{4}$ on the interval $0 \le x \le 2\pi$, 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'
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 $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
A. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are $f(\boxed{\text{ }}) = \boxed{\text{ }}$, $f(\boxed{\text{ }}) = \boxed{\text{ }}$, and $f(\boxed{\text{ }}) = \boxed{\text{ }}$
B. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are $f(\boxed{\text{ }}) = \boxed{\text{ }}$ and $f(\boxed{\text{ }}) = \boxed{\text{ }}$
C. The function has a local maximum at one value of x. The maximum value is $f(\boxed{\text{ }}) = \boxed{\text{ }}$
D. There are no local maxima
