Find the absolute extrema:

$\displaystyle f(x) = sin x- cos x ; [0, \pi]$

Okay. So first I found the derivative of $\displaystyle f(x)$

$\displaystyle

f ' (x) = cos x + sin x$

Then, to find the critical points I must set this to zero.

$\displaystyle cos x + sin x = 0$

But I'm a little confused. If they were multiplying, I would do: either cos x = 0 or sin x = 0, right ? But since they're being added, I'm not really sure how to get x = ? so I can continue with the question.