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Find the equation of the tangent line

  1. Dec 28, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the equation of the tangent line to the curve 3xy = x^3 + y^3 at point (2/3,4/3)


    2. Relevant equations



    3. The attempt at a solution

    I found the deriviative to be 3x^2-3y / 3x - 3y^2 which i simplified to x^2 - y / x - y^2

    I found the slope of at those points to be - 1/2

    Then using the y - y1 = m(x - x1) formula I got 3x + 3y - 10 = 0 for the equation.

    What do you guys think?
     
  2. jcsd
  3. Dec 28, 2008 #2
    Looks good, however, at the point (x,y) = (2/3, 4/3), the slope of the graph is 4/5, not -1/2.
     
  4. Dec 28, 2008 #3

    Dick

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    Science Advisor
    Homework Helper

    I agree. I think you are having problems with ratios of fractions.
     
  5. Dec 28, 2008 #4
    Thank you for the help guys, I got 4x - 5y + 4 = 0 for the equation. What do you think?
     
  6. Dec 28, 2008 #5
    Perfect. :)
     
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