Find asymptotes, extrema and inflection points for y = xe^(1/x) and y = xe^(-x)

[drhope1]

HELP! Please! I only have 1 more day to figure this out!

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
2) relative extrema
3) inflection points
4) intervals where the function is increasing/decreasing
5) where the function is concave up/down

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...)

 

[kreil]

to find the asymptotes, try graphing the functions

to find extrema, take the derivative of each function (using the chain rule..) and set it equal to zero. then see which values of x make the derivative zero. if the derivative goes from - to + through the zero, it is a relative min. If it goes from + to -, it is a relative max.

inflection points are the zeroes of the second derivative.

if the value of the first derivative is positive, the fcn is increasing. if it is negative, the fcn is decreasing.

the fcn is concave up/down at the relative extremum points (concave up for a relative min, concave down for a relative max)

good luck