Calculus: Determine the constants from function

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The function h(x) = x^3 + bx^2 + d has a critical point at (2, -4). Determine the constants b and d and find the equation of h(x).

IM SO CONFUSED :(

  • Calculus: Determine the constants from function -

    dh/dx = 0 at critical points

    dh/dx = 3 x^2 + 2 b x = 0
    x (3x+2b) = 0
    so
    at (2,4), 3x+2b = 0 = 6 + 2b
    so b = -3
    so
    h = x^3 -3 x^2 + d
    at x = 2, h = -4
    -4 = 8 - 12 + d
    d = 0
    so
    h = x^3 -3 x^2

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