This is of course a vector-valued derivative because q is a vector-valued function. At the beginning and end of the curve, the values of the derivatives are Graphically, this means that the curve q (u) starts at u = 0 traveling in the direction of the vector from p0 to p1. Similarly, at the end, where u = 1, the curve q (u) is tangent to the vector from p2 to p3