calculus

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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^2-4x)^-1)

Thank you!

  • calculus -

    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

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