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Homework Help: Marginal cost and marginal revenue

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data

    For a certain product, cost C and revenue R are implicitly given as follows, where x is the number of units sold (in hundreds)
    a) Find and interpret the marginal cost dC/dx at x=5
    b) Find and interpret the marginal revenue dR/dx at x=5

    2. Relevant equations

    C2 = x2+100√x +50
    900(x-5)2 + 25R2 = 22500

    3. The attempt at a solution

    So I think I'm making this out to be a lot harder than it actually is. My first instinct would be to apply derivatives and chain rule.
  2. jcsd
  3. Oct 24, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Why don't you just go ahead and do that, to see what you get?

  4. Oct 24, 2012 #3
    Okay, so then because C defines x implicitly, we'll be looking for implicit derivatives, right? So with that, I get my marginal cost to be

    c'= (2x + 50/√x)/2c

    And then from there, I would plug in my x=5

    But I'm thinking that equation might be wrong? Because what would I do with the 2c in the denominator?
  5. Oct 25, 2012 #4


    Staff: Mentor

    What you have looks OK, except that you should have parentheses around 2C in the denominator.

    Use the cost equation to find C when x = 5, and then find C'(x).
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