Vertical tangent line

  • Thread starter sonofjohn
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  • #1
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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.
 

Answers and Replies

  • #2
76
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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?
 
  • #3
HallsofIvy
Science Advisor
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Yes, of course. I was wondering why you were setting "x= 0" before.
 

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