Conjugate points of extermals of functional

[braindead101]

Show that the extermals of any functional of the form integ (a->b) F(x,y') dx have no conjugate points.

Not sure how to start this question, any help would be appreciated

 

[braindead101]

anyone know how to do this?

 

[HallsofIvy]

One of the reasons we ask that people show what they have done is to understand exactly what their problem is. I understand from your title that you are working in the calculus of variations but even so there are many different definitions of "conjugate". Exactly what is your definition of "conjugate point"?