To see two quintic polynomial patches become a continuously differential surface, check :-) . Check also :-) :-) and :-) :-) :-) .

To see two quintic polynomial patches become a twice continuously differential surface, click :-) . Check also :-) :-) .

To see two quintic polynomial patches are only C^1 smooth surface, click :-) :-) . You may not be able to determine if those two patches are NOT twice continuously differentiable unless you look at the geometric meaning of the control net over the surface.

To see two quintic polynomial patches become a C^3 smooth surface, click :-) Check also :-) :-) here.

To see two quintic polynomial patches become a C^4 smooth surface, click :-) . Check also :-) :-) .