calculus

find the equation of the curve for which y''=6x-4 and which passes through (1,2) and (-2,5).

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  1. y"= 6x-4
    y' = 3x^2 - 4x + a
    y = x^3 - 2x^2 + ax + b

    y(1) = 2 and y(-2) = 5, so

    1-2+a+b = 2
    -8-8-2a+b = 5

    a = -6, b=9, so

    y = x^3 - 2x^2 - 6x + 9

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