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Math Help - Maximum profit - Calculus (urgent!)

  1. #1
    Newbie melanie's Avatar
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    Maximum profit - Calculus (urgent!)

    If profit is given by:

    p(x) = 280x - 3x^3 + 5x ln(x)

    The average profit form would be:
    = p(x) / x

    = 280 - 3x^2 + 5 ln(x)
    ___________________

    now, how do i determine how many units should be produced so the average profit is a max ?!
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  2. #2
    Newbie melanie's Avatar
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    I'd really appreciate it if anyone can tell of if I'm on the right track!

    For a maximum point, f'(x) = 0 and f"(x) < 0

    Therefore:
    We find the first and the 2nd derivate of the AVERAGE profit function:

    P'(x) = - 6x + 1/x = 0
    P"(x) = [ -6 - 1/x^2 ] < 0

    IS this right so far?!!

    I'm really confused.
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