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Find points on a curve when slope is 0

  1. Apr 19, 2015 #1
    The problem statement, all variables and given/known data
    Find the points on the curve xy^2+x^2y=16 when the tangent line is horizontal

    The attempt at a solution
    I found the derivative of the curve
    -(y(2x+y))/(x(x+2y))
    then I found what values of y make the derivative equal 0
    y=0,-2x
    Then I went to plug into the original curve to find x and that is where I got lost. I do not know how to isolate x in this case.
     
  2. jcsd
  3. Apr 19, 2015 #2

    LCKurtz

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    The first thing you should notice is that ##y=0## doesn't give a point on the graph. But what happens if you put ##y=-2x## into the original equation?
     
  4. Apr 19, 2015 #3
    Thanks! Got it now.
     
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