$f(x)= 9\cos^2(x) - 18\sin(x),\quad 0 \le x \le 2\pi$
(a) Find the interval on which $f$ is increasing.
I answered: $(0, \frac {3\pi}{2})$
(b) Find the interval on which $f$ is decreasing.
I answered: $(\frac {3\pi}{2}, 2\pi)$
(c) Find the local minimum and maximum of $f$.
First off, am I correct with a and b? Second, I am getting really weird values when I test values on my derivate. For example: $\frac {\pi}{2}$ entered into the derivative returns $0$. Whereas if I was to enter $\pi$ I get a positive value($18$). How do I find the minimum and maximum of this function?