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Relative Extrema

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data

    The cost of producing x units is given by:

    f(x)=800+110x-110ln(x)

    Find the minimum average cost. x >= 1



    2. Relevant equations

    Cost=f(x)/x

    Marginal cost is C'(x)


    3. The attempt at a solution

    This is what I have done so far:

    C(x)=(800+110x-110ln(x))/x

    C'(x)= (110ln(x)-910)/x^2

    setting C'(x)=0

    I get x=e^(910/110)

    C''(x)=(1930-220ln(x))/x^3

    Plugging in my value for x I get an increasing number validating, or I thought my x=value. Webwork tells me that e^(910/110) is incorrect for the minimum cost.
     
  2. jcsd
  3. Mar 26, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    This derivative is incorrect. Please show how you got it, step by step.


     
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