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Differentiation equation curve

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data

    A curve has equation [tex]y = Ax^3 + Bx^2 + Cx + D[/tex], where A, B, C and D are constants.
    Given that the curve has gradient -4 at the point (1,2) and gradient 8 at the point (-1,6), find A, B, C and D.

    2. Relevant equations



    3. The attempt at a solution

    [tex]y = Ax^3 + Bx^2 + Cx + D[/tex]
    [tex]dy/dx = 3Ax^2 + 2Bx + C[/tex]
    [tex]-4 = 3A + 2B + C[/tex] (1)
    [tex]8 = 3A - 2B + C[/tex] (2)
    [tex]-12 = 4B[/tex](3) = (1)-(2)
    [tex]B = -3[/tex]

    Right here is where I get stuck. If i eliminate A or C, they both go at the same time :S. I think I'm missing a trick here or something.

    hope you can help

    thanks
     
    Last edited by a moderator: Jul 9, 2014
  2. jcsd
  3. Oct 17, 2007 #2

    Hurkyl

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    Is there any information in the problem you haven't used?
     
  4. Oct 17, 2007 #3
    o wait, do i like substitute the y values in from the co-ordinates given?
     
  5. Oct 17, 2007 #4
    right, did that, now i have D and B, but still cant get to the A and C because they always seem to cancel each other out when i stick them in simeltaneous equations :S


    ahhh
     
  6. Oct 17, 2007 #5

    Hurkyl

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    Maybe you're accidentally using the same equations twice? Now that you know B and D, try starting over and use all four equations again. (But plug in the known values for B and D)
     
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