Question: For the following functions, find the critical points, determine their nature (maxima, minima, inflection, etc.) and sketch the graph or surface:

1. \(f(x)=\frac{x}{1+x^{2}}\) for \(x \neq 0\),
2. \(\quad g(x)=|x| e^{-|x-1|}\),
3. \(\quad F(x, y)=\left(x^{2}-4\right)^{2}+y^{2}\),
4. \(\quad G(x, y)=\sin x \sin y \sin (x+y) \quad(0 \leq x, y \leq \pi)\).

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