If there is ANYONE out there who is a kind enough person to help me with this (and knows how to do it!) I would be VERY grateful!! I only have one more day to work on these problems!! Thank you so much!

For the following functions:

a) y = xe^(1/x)

b) y = xe^(-x)

I need to find:

1) vertical and horizontal asymptotes.

Mr F says: See main reply.
2) relative extrema

3) inflection points

4) intervals where the function is increasing/decreasing

5) where the function is concave up/down

Mr F says: Do you know how to find dy/dx? Do you know how dy/dx relates to the above?
Be sure to evaluate limits at the borders of the domain of the function (e.g. infinity, negative infinity, one sided limits around vertical asymptotes...)