QPaperGen

We have \( f(x) = \sin x + \cos x \)

\[
f'(x) = \cos x - \sin x \\
f'(x) = 0 \Rightarrow \sin x = \cos x \Rightarrow \tan x = 1 \Rightarrow x = \frac{\pi}{4}
\]

Now evaluate \( f \) at endpoints and critical points:
\[
f\left( \frac{\pi}{4} \right) = \sin \frac{\pi}{4} + \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2} \\
f(0) = \sin 0 + \cos 0 = 1 \\
f(\pi) = \sin \pi + \cos \pi = -1
\]

\(\textbf{Absolute maximum}\) is \( \sqrt{2} \) at \( x = \frac{\pi}{4} \) and \(\textbf{Absolute minimum}\) is \( -1 \) at \( x = \pi \)