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Implicit Differentiation and coordinates

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the coordinates of the point in the first quadrant at which the tangent line to the curve x3-xy+y3=0 is parallel to the x-axis.

    SO:
    x= +
    y= +
    mtan=0

    2. Relevant equations

    [tex]\frac{dy}{dx}=m_{tan}[/tex]

    3. The attempt at a solution

    [tex]\frac{dy}{dx}=\frac{y-3x^{2}}{3y^{2}-x}=0[/tex]

    After I get the derivative, I have no clue what to do.
     
  2. jcsd
  3. Oct 26, 2008 #2
    you have two equations two variables so solve for one of the variables
     
  4. Oct 26, 2008 #3

    Dick

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    Science Advisor
    Homework Helper

    For the derivative to equal zero x and y must satisfy y-3x^2=0, right? But x and y must also be on the curve so x^3-xy+y^3=0. That's two equations in two unknowns. Solve them.
     
  5. Oct 26, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You now have two equations to solve for x and y. Oh, and here's a simplification:
    a fraction is 0 only when its numerator is 0.

    Blast! I walked away from the computer and Dick got in ahead of me!
     
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