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Where am I going wrong on implicit differentation?

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Determine the equation of a tangent line to a curve at the given point.

    3x2+xy+2y2=36 , P(2,3)

    2. Relevant equations



    3. The attempt at a solution

    3x2+xy+2y2 = 36

    finding the derivatives of each term I get:

    6x+xy'+y+4yy' = 0
    xy'+4yy' = -6x-y
    y'(x+4y) = -6x-y
    [tex]y' = \frac{-6x-y}{x+4y}[/tex]
    Which gives me a slope of 1.5 after plugging (2,3) in to the equation.

    Then for the tangent: y-3=1.5(x-2) , y=1.5x

    Somewhere I went wrong because this is not the right answer.
     
  2. jcsd
  3. Oct 11, 2011 #2
    Haven't looked at it carefully, but slope should be -1.5, after substitution.
     
  4. Oct 11, 2011 #3
    Try replugging your point (2,3).
     
  5. Oct 11, 2011 #4
    [tex]\frac{-6(2)-3}{2+4(3)}=\frac{-15}{14}[/tex]

    I copied the wrong sign down.
     
    Last edited: Oct 11, 2011
  6. Oct 11, 2011 #5
    if you plug in (2,3) you get -15 / 14 for the slope.
     
  7. Oct 11, 2011 #6
    Thanks for your help, I don't know why I can't seem to find my mistakes when going back through the problem. I even copied it down wrong on here as I was saying right outloud to myself.

    Once again Thanks.
     
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