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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.

    x= +
    y= +

    2. Relevant equations


    3. The attempt at a solution


    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


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    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


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    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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