let u=(cost, sint, 0) be a tangent vector of the surface at 0, since 0 is a critical point.

The curve cut by the normal plain through u is ( s cost, s sint, s^2), its tangent vector is T=(cost, sint, 2s), accelerator is A=( 0, 0, 2),

since |T|=1 at 0, so A(0) is the curvature vector, and its length 2 is the curvature. It is constant for all t.