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Vertical tangent line

  1. Jan 13, 2009 #1
    The curve defined by x3 +xy - y2 = 10 has a vertical tangent line when x = ?

    To find when the tangent line is vertical, could I find when the slope is undefined for the original function? The way I previously tried this problem was by taking the first derivative and then finding when x = 0. That is one of the multiple choice answers but that cannot be right, for that would find the horizontal tangent and not the vertical tangent line.
     
  2. jcsd
  3. Jan 13, 2009 #2
    Now that I think about it couldn't I find where the slope is undefined by finding where the first derivative is undefined?

    If I have

    dy/dx = (-3x^2 - x)/(x-2y)

    could I set the denominator = 0 and solve?
     
  4. Jan 13, 2009 #3

    HallsofIvy

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    Staff Emeritus
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    Yes, of course. I was wondering why you were setting "x= 0" before.
     
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