\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f(x) = xe^{-x}\).
  1. Find expressions for \(f'(x)\) and \(f''(x)\).
  2. Find the coordinates of the stationary point and determine its nature.
  3. Find the coordinates of the point of inflection.
  4. Find the interval(s) where the graph of \(f\) is concave down.

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