I would greatly appreciate any help for this problem for my Calc 3 class:
Determine whether the given surface is smooth, piecewise smooth or neither.
I took the derivative with respect to u, r(u):
And then with respect to v, r(v):
I then did the cross product, r(u) x r(v)
And I got <2uv+6u^2, -6v, -6>
Since this never equals 0, we can say that the surface is always smooth. Does that look correct?