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Implicit differentiation

  1. Apr 21, 2007 #1
    Question:

    Find the co ords of the turning points of y^3 + 3xy^2 - x^3 = 3

    Attempt:

    (differentiate w.r.t. x)
    d/dx(y^3 + 3xy^2 - x^3) = d3/dx

    3y^2(dy/dx) + 3(2xy(dy/dx) + y^2) - 3x^2 = 0

    (divide through by 3)

    y^2(dy/dx) + 2xy(dy/dx) = x^2 - y^2

    (take dy/dx as a comon factor)

    dy/dx(y^2 + 2xy) = x^2 - y^2

    dy/dx = (x^2 - y^2)/(y^2 + 2xy)

    now to find turning points, you set dy/dx = 0
    but with explicit differentiation, theres only one variable, but theres 2 here, so im stuck :/
     
    Last edited: Apr 21, 2007
  2. jcsd
  3. Apr 21, 2007 #2

    HallsofIvy

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    Staff Emeritus
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    "Turning points" must occur where dy/dx= 0 (though not all such points are turning points.

    If dy/dx = (x^2 - y^2)/(y^2 + 2xy) and y^3 + 3xy^2 - x^3 = 3, can you solve those two equations for x and y?
     
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