QPaperGen

\[
h(x) = \sin x + \cos x \Rightarrow h'(x) = \cos x - \sin x
\]
\[
h'(x) = 0 \Rightarrow \cos x = \sin x \Rightarrow \tan x = 1 \Rightarrow x = \frac{\pi}{4}
\]
\[
h''(x) = -\sin x - \cos x < 0 \Rightarrow \text{Local maximum at } x = \frac{\pi}{4}
\]
\[
h\left( \frac{\pi}{4} \right) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2}
\]