QPaperGen

\[
g'(x) = \frac{-2x}{(x^2 + 2)^2}
\Rightarrow g'(x) = 0 \Rightarrow x = 0
\]

Check sign change:
- For \( x < 0 \), \( g'(x) > 0 \)
- For \( x > 0 \), \( g'(x) < 0 \)

So by first derivative test:
\[
x = 0 \text{ is a local maximum}
\Rightarrow g(0) = \frac{1}{2}
\]