5. Consider the function $f(x) = xe^{-x}$. Keeping in mind that an expression of the form $a^b$ is positive whenever a is positive, determine the following:
• where f is increasing and decreasing;
• where f is concave up and down;
• all x and y intercepts;
• all points of inflection;
• all relative extrema, classified by clearly explained use of the Second Derivative Test.
Answers to all parts should be boxed.
Then, aided by the additional information that the x-axis is a horizontal asymptote, draw a graph of $y = f(x)$. All points determined above should be labeled with their coordinates on the graph.
Continue onto the next page as necessary.
