Note: For any questions that asks you to enter all values, enter a list separated by commas. If there are no such values, enter “None”. Let $\displaystyle{ f(x) = {x^{2}e^{x}} }$

1. Determine the intervals on which $f$ is concave up and concave down. interval
   • $f$ is concave up on:
   • $f$ is concave down on:
2. Based on your answer to part a, determine the inflection points of $f$. Each point should be entered as an ordered pair (that is, in the form $(x, y)$).
   The inflection points are
3. Find the critical numbers of $f$ and use the Second Derivative Test, when possible, to determine the relative extrema. List only the $x$-coordinates.
   • Relative maxima at $x=$
   • Relative minima at $x=$