Rath on 28 January 2010
http://library.wolfram.com/webMathematica/Education/WalkD.jsp
http://en.wikipedia.org/wiki/Second_derivative_test
With those two links you should be able to do most of it easy peasy.
Edit: Points of inflection can be found where f'' = 0
Asymptotes can be found by turning the equation into a whatdayacall it, when you have only a numerator and denominator, and then solve the top for zero which is your horizontal asymptotes and the bottom for zero which are your verticle asymptotes. By the looks of the graph they're about the origin though. At least I think that should work.
