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10 June, 06:20

Find the minimum value of the average cost for the given cost function on the given intervals. Upper C (x) equals x cubed plus 33 x plus 432 a. 1 less than or equals x less than or equals 10 b. 10 less than or equals x less than or equals 20

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  1. 10 June, 10:16
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    C (x) = x^3 + 33x + 432

    average cost, Ca = C (x) / x

    Ca = x^2 + 33 + 432/x

    To find the minimum, we look at the critical numbers

    differentiation C (x) = 2x - 432/x^2 = 0

    multiplying by x^2

    2x^3 - 432 = 0

    x = 6

    x lies in the interval [1, 10}
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