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

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Answer 1 · 2015-04-16T00:21:37

$y = sin x + cos x = sqrt2*sin (x + pi/4).$
$sin (x + pi/4)$ has max at $(1)$ and $(-1)$ .
Then, $y$ has max at $(sqrt2)$ and $-(sqrt2).$

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