Question: If \(f(x)=\frac{3 x^{2}}{x^{2}+5} \quad f^{\prime}(x)=\frac{30 x}{\left(x^{2}+5\right)^{2}} \quad f^{\prime \prime}(x)=\frac{30\left(5-3 x^{2}\right)}{\left(x^{2}+5\right)^{3}}\)

1. Determine the intervals where \(f(x)\) is increasing and where it is decreasing.
2. Find all local maxima and all local minima.
3. Determine where \(f(x)\) is concave up and where it is concave down.
4. Find all inflection points.
5. Find all horizontal asymptotes and all vertical asymptotes.
6. Sketch the graph of \(f(x)\).

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