calculus
posted by Chelsea .
I have three questions I'm having a terrible time with:
1)Find, if possible, the absolute maximum value and where it occurs for f(x)=ln(xe^x) on (0,infinity).
2)Find the value(s) of "c" guaranteed by the Mean Value Theorem for the function f(x)=ln(x^2) on the interval [1,e].
3)Find the derivative of the following function: h(x)=ln(((3x+1)(2)^1/2))((5x^24x)^1)
Thank you!

y = ln (x e^x)
y' = (1/(x e^x) ) * [ x (e^x) + e^x ]
= 1 + 1/x
that derivative is zero when x = 1
then xe^x = .36788
what is the second derivative?
y'' = 0  1/x^2
humm, when x = 1
curvature is  so that is a maximum and the only one I see