Tangent Planes: Existence & Extensibility

[Char. Limit]

Most functions y=f(x) have tangent lines for any point x.

Does a function z=f(x,y) have a tangent plane for any point x,y?

And could you extend this to higher dimensions if necessary? (Tangent cubes? Tangent hypercubes?)

Edit: Sorry, I thought I was posting in the General Math forum. Movement would be helpful, please.

 

[Eynstone]

Yes. Check out -http ://mathworld.wolfram.com/TangentPlane.html