Mathematics

The gradient of a curve is defined by

dy/dx = 3x^(1/2) - 6

Given the point (9, 2) lies on the curve, find the equation of the curve

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  1. y' = 3x^(1/2) - 6
    y = 2x^(3/2) - 6x + C
    y(9) = 2, so

    2*27 - 6*9 + C = 2
    C = 2

    y = 2x^(3/2) - 6x + 2

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