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!