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More Implicit Differentiation Help

  1. Jul 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the tangent line to x^3 + y^3 - 6xy = 0 at the point ((4/3), (8/3))


    2. Relevant equations
    I got y = -(8/5)x + (24/5). Is this correct?


    3. The attempt at a solution
    Lots of algebra involved. Sorry. but I'd rather not type it. I take the derivative of each term and eventually get:

    [-3x^2 - 6y] / [3y^2 - 6x].

    This simplifies to:

    [x^2 + 2y] / [2x - y^2].

    I substitute the stuff in appropriately, I get m = -(8 / 5).

    Then I do:

    y - (8/3) = -(8 / 5)(x - (4/3)).

    I ask because Wolfram Alpha disagrees with me:
    http://www.wolframalpha.com/input/?...3+++y^3+-+6xy+=+0+at+the+point+((4/3),+(8/3))
     
  2. jcsd
  3. Jul 12, 2012 #2

    Mentallic

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    Homework Helper

    You're off by a sign, it should be

    [tex]\frac{dy}{dx}=\frac{6y-3x^2}{3y^2-6x}[/tex]
     
  4. Jul 12, 2012 #3
    I see. I didn't distribute a "- 6" to a "+ y" properly. Thanks.
     
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