Hello All,

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.

r(u,v)=<3u,u^2-2v,u^3+v^2>

I took the derivative with respect to u, r(u):

<3,2u,3u^2>

And then with respect to v, r(v):

<0,-2,2v>

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?