Calculus

The marginal cost for producing x units of a certain product is given by the formula MC = 0.001x^2-0.5x+66.5. A. What is the increase in the cost of the production if the production level is raised from 200 to 400 units? B. What is the average cost per item of producing 330 items.

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  1. marginal cost is the derivative of cost with x. the cost of one more at number x
    so
    integrate your function

    C(x) = (.001/3)x^3 - (0.5/2)x^2 + 66.5 x + k
    assume when x = 0, c = 0 so k = 0 (not really true because you have to set up to build the first one but you need that for part B)

    at x = 400
    C(400)=(.001/3)(400)^3 - (0.5/2)400^2 + 66.5 (400)
    C(300) = same with 300
    subtract

    average = total C(330)/330

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