Consider the integral I with integrand F(x,y,y'), limits a,b with y(b) undetermined.
(1) Derive both the Euler-Lagrange equation and the endpoint condition that 'partial' df/dy' vanishes at b.
(2) Use this result to show that the shortest distance from the origin to the line x = 1 lies
along the line y = 0.
I have done question (1). I included it for context. For (2) I am not sure what the functional is.