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Show that f(x) = x^3 and g(x) = 200x^3 grow at the same rate.

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  1. If by "same" you mean the same percentage per unit time, then
    f'/f = 3x^2/x^3
    g'/g = 600x^2/200x^3 = 3x^2/x^3

    Naturally, since g started out with 200 times as much, its actual growth rate is 200 times as much as f's.

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