Finding the Vertical Tangent Line of x3 + xy - y2 = 10 Curve

[sonofjohn]

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.

 

[sonofjohn]

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?

 

[HallsofIvy]

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