Well because of an exercise involving a curve and a point not in that curve I found out that the minimum of the distance between the curve and the point is found at a point such that the derivative of the curve vector is perpendicular to the vector (curve-external point vector). I could find it cause being the curve X(t) and the point P the distance between the curve and the point is abs(X(t)-Q) and setting the derivative to zero to get the critical point we get that to have a critical point X'(t) is perpendicular to X(t)-Q but i cant prove thats a minimum and not a maximum... how can i do it?

help would be apreciated...thanks