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Math Help - Finding the equation of a cubic from given information

  1. #1
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    Finding the equation of a cubic from given information

    one last question:

    The graph of the function y = ax^3 + bx^2 + cx + d has a maximum turning point at (0,1) and a minimum turning point at (-2, -2). Find the values of the coefficients.

    I managed to get c = 0 and 3a - b = 0, but thats it..help?
    Last edited by mr fantastic; August 24th 2009 at 02:34 AM. Reason: Moved from another thread
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  2. #2
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    Quote Originally Posted by duskmantle View Post
    one last question:

    The graph of the function y = ax^3 + bx^2 + cx + d has a maximum turning point at (0,1) and a minimum turning point at (-2, -2). Find the values of the coefficients.

    I managed to get c = 0 and 3a - b = 0, but thats it..help?
    (0, 1) on curve: 1 = d .... (1)

    (-2, -2) on curve: -2 = -8a + 4b - 2c + d .... (2)

    \frac{dy}{dx} = 3a x^2 + 2bx + c.

    \frac{dy}{dx} = 0 when x = 0: 0 = c .... (3)

    \frac{dy}{dx} = 0 when x = -2: 0 = 12a - 4b + c .... (4)

    Solve the above equations simultaneously for a, b, c and d.
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