Sketch the curve.
$y = xe^{-1/(x+1)}$
Only use technology if absolutely needed, and only then to approximate values. Do not use graphing technology.
• Label the $y$-intercept, $x$-intercept(s) (if analytically possible), all local extrema, and all inflection points on your final graph.
• Use calculus to determine the behavior of the graph near any vertical asymptotes.
• Use calculus to determine any horizontal or oblique asymptotes. If oblique asymptotes exist, prove that they are oblique asymptotes.
• Be sure to graph any and all asymptotes.
• Finally, credit is awarded for a clean, precise graph.