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Homework Help: Implicit differentitaion and finding coordinates

  1. Jan 11, 2009 #1
    1. The problem statement, all variables and given/known data

    dy/dx = [3(x^2)y - y^2] / [2xy - x^3]

    Find the x-coordinate of each point on the curve where the tangent line is vertical.

    2. Relevant equations

    original equation is x(y^2) - (x^3)y = 6

    3. The attempt at a solution

    i set the denominator of the deriv. to 0, but i have no idea where to go from there. am i solving for x or y? is there a way i can eliminate one of the variables? do i need to plug anything into the orig. equation?
  2. jcsd
  3. Jan 11, 2009 #2
    You have two equations and two variables so it shouldn't be difficult to get what you need. Setting the denominator to zero, you can solve for y. Then using the original equation, you can solve for x.
  4. Jan 11, 2009 #3
    i don't know how to solve for y using the equation x(y^2) - (x^3)y = 6....i get stuck
  5. Jan 11, 2009 #4


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    Gold Member

    Try this: the denominator equals x(2y - x^2), therefore, using the zero product property, the denominator is equal to zero when x = 0 and 2y = x^2. Use the second equation with the original to determine which values of x and y work.
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