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Math Help - The Fundamental Theorem of Calculus

  1. #1
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    The Fundamental Theorem of Calculus

    Hello all, I have 2 questions and if you could help me and explain them I would appreciate it so much. Thank you!

    1. The marginal cost C′(q) (in dollars per unit) of producing q units is given in the following table.
    (a) If fixed cost is $12,000, estimate the total cost of producing 400 units.
    (b) How much would the total cost increase if production were increased one unit, to 401 units?
    q 0 100 200 300 400 500 600
    C′(q) 24 20 15 17 22 32 38
    I found the answer of (a) which is 19,500 but how do I find (b) without a function to plug into my integral?

    2. The graph of a derivative f′(x) is shown in Figure 5.67. Fill in the table of values for f(x) given that f(0) = 2.
    x 0 1 2 3 4 5 6
    f(x) 2
    Figure 5.67 Graph of f′, not f

    I have no idea how to even start this one. Please help me!
    Last edited by kuppina; January 24th 2013 at 05:26 PM.
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  2. #2
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    Re: The Fundamental Theorem of Calculus

    Isn't that exactly what "marginal cost" means?
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  3. #3
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    Re: The Fundamental Theorem of Calculus

    Quote Originally Posted by HallsofIvy View Post
    Isn't that exactly what "marginal cost" means?
    Wouldn't I have to find how much it is to make one item which would be C'(q)? Except i'm not given any kind of formula that would allow me to find the derivative.
    Last edited by kuppina; January 24th 2013 at 06:00 PM.
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