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Math Help - Marginal Cost Calculus Help

  1. #1
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    Marginal Cost Calculus Help

    Can someone help me out with some Business Calculus... It's from a calculus class but it is also used in economics. The basic term is marginal cost.

    if C' (x) = -0.0006x^2-0.12x+120

    How can i find the intervals where it increases and decreases? I'm thinking of factoring it but i'm not sure how to proceed...
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  2. #2
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    You have a function that you believe to be representative of Marginal Cost. Your task is to determine where this function is increasing or decreasing.

    You should let this description roll around a bit in your brain. This is an ideal question for a derivative. Derivatives provide this kind of information.

    Expressed as a function of x, C'(x) = -0.006x^2 - 0.12x + 120

    We need the derivative of C'(x) - this is the second derivative of C(x). C"(x) = -0.012x - 0.12

    You should be able to figure out where C"(x) is positive, negative, or zero.

    One more thing: As C(x) may describe a real quantity, you will need to consider it's Domain. I'm guessing x >= 0. Is there an upper limit?
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  3. #3
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    yes it states in the problem that 0 <= x < = 300 . I figured the problem. Thanks a lot! I didn't know we had to do the second derivative but it made much more sense after that.
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