# How do you find all extrema in the interval [0, 2(pi)] for y= sin x + cos x?

$y = \sin x + \cos x = \sqrt{2} \cdot \sin \left(x + \frac{\pi}{4}\right) .$
$\sin \left(x + \frac{\pi}{4}\right)$ has max at $\left(1\right)$ and $\left(- 1\right)$.
Then, $y$ has max at $\left(\sqrt{2}\right)$ and $- \left(\sqrt{2}\right) .$