QPaperGen

\[
f(x) = \sin x - \cos x \Rightarrow f'(x) = \cos x + \sin x
\]
\[
f'(x) = 0 \Rightarrow \cos x = -\sin x \Rightarrow \tan x = -1
\Rightarrow x = \frac{3\pi}{4}, \frac{7\pi}{4}
\]

Second derivative:
\[
f''(x) = -\sin x + \cos x
\]

At \( x = \frac{3\pi}{4} \),
\[
f''\left( \frac{3\pi}{4} \right) = -\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} = -\sqrt{2} < 0
\Rightarrow \text{Local maximum}
\]
\[
f\left( \frac{3\pi}{4} \right) = \frac{1}{\sqrt{2}} - \left( -\frac{1}{\sqrt{2}} \right) = \sqrt{2}
\]

At \( x = \frac{7\pi}{4} \),
\[
f''\left( \frac{7\pi}{4} \right) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2} > 0
\Rightarrow \text{Local minimum}
\]
\[
f\left( \frac{7\pi}{4} \right) = -\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} = -\sqrt{2}
\]