Recent content by Gux

I think I am strating to understand... In case you know (x1), y(2), y'(x1) and y'(x2): in the limit, the shortest way is a straight line: the part of the curve around the point x1 should change to obtain the given derivative y1(x1), but "in the limit" this part of the curve disappears. So the...

Yes, the solution is unique Thank you: (1) Ok, so if we impose only the derivatives, we have a family of solutions. How to find them? (2) How to find the solution in case we impose y(x1), y(2), y'(x1) and y'(x2)?

But... Thank you for your reply, but: Imagine you want to find the shortest way y(x) between two points (x1,y1) and (x2,y2), given that y'(x1)=0 and y'(x2)=1. Obviously there is a solution. How to find it?

Minimizing a functional: When you know the values of the function y(x) on the boundary points y(x1) and y(x2), minimizing the functional ∫{L(x,y,y')} yields the Euler-Lagrange equation. How can you minimize the functional if, instead, you know the derivatives y'(x1) and y'(x2)? What if...