How to Find a Tangent Plane on a Surface with Positive Z Values?

[Tony11235]

The problem is find a parametrization of the surface x^3 + 3xy +z^2 = 2, z > 0, and use it to find the tangent plane at the point x=1, y=1/3, z=0. How is this possible when z > 0? I found a parametrization but when I plug the point in the x and the y places are undefined.

 

[CarlB]

(a) A tangent plane can exist at a point that is in the closure (it's been 30 years, since topology class, is that the right term?) of the surface, so it is possible.

(b) What is the parameterization you found? My inclination would be to define y in terms of x and z but sometimes I guess wrong.

Carl

 

[Tony11235]

Nevermind. I think I know what to do now. Thanks anyway.