Finding the maximum and minimum

Use analytic methods to find the extreme values of the function on the interval and where they occur.

Extreme values includes local and absolute max and min.

Analytic methods meaning I can't graph anything.

$\displaystyle g(x)= \sin (x + \frac{\pi}{4})$

To find the critical points i need to find when y'= 0.

$\displaystyle g'(x)=\cos(x + \frac{\pi}{4})$

I got the points $\displaystyle \frac{\pi}{4}, \frac{5\pi}{4}$

When plugged into g(x) they yield 1 and -1, respectively.

These are only 2 critical points; I need 4.

Thanks for the help!