Hi, I've been revising the calculus of variations and using the wiki entry on the euler lagrange equation (http://en.wikipedia.org/wiki/Euler-Lagrange_equation) as a reference. Scroll down and you'll see: Derivation of one-dimensional Euler–Lagrange equation. Expand this. In it you'll see the statement: "It follows from the total derivative that" and:
dF/dε= dx/dε*∂F/∂x + dgε/dε*∂F/∂gε + dg'ε/dε*∂Fε/∂g'ε
What happened to the first term (dx/dε*∂F/∂x)?
The Attempt at a Solution
I understand that the first term has gone to zero. But how? If π(a) and π(b) both = 0 surely f(x) is a line with f(x) = 0? In which case it is clear that that term will go to zero.