Question: Let \(f\) be the function defined by \(f(x)=3 x e^{-x}\) for all real numbers \(x\).

1. Find equations of all asymptotes to the graph of \(f\). Show work.
2. Find the \(x\) -coordinate of each critical point of \(f\). For each critical point, determine whether it is a relative maximum, a relative minimum, or neither. Justify your answers.
3. Describe the concavity of the graph of \(f\).
4. Using the results found in parts (a), (b), and (c), sketch the graph of \(y=f(x)\).

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