I have solved for the parameterization of a curve of intersection of two surfaces. I basically need to find the directional dirivative to solve for a rate of change in a scaler field. I know how to do this but I have a question on how to assign t=0 to the parameterized curve of intersection. I am given at the point of interest (t=0) pt=(2,-1,1)
and the speed at t=0 = 6. The curve is R(t)=f(t)i+f(t)j+tk. I know I need the velocity tangent at the point which is V/|V|. How do I use the pt and initial speed to get there?

Thanks in advance.