(a) Find the extremal for the following:

i.e. satisfying

(1)

(b) For the extremal , show that

(2)

for all with .

(Hint: Multiplying equation (1) with , integrating in yields

(3)

and then integrating by parts in (3) with and .

(c) prove that is a minimizing curve.

(Hint: use inequality for any two real number . Then you use the identity (2).)