Hello everyone,

I have another question involving extremals. There are 3 parts to it, and trickier than my last post.

(a) Find the extremal for

i.e. satisfying

(b) For the extremal show that

for all

Hint: and

(c) Prove that is a minimizing curve.

My Working(haven't made much progress)

(a) Applying the Euler-Lagrange equation

which has solution

Now

and

so

which is really as far as I've gotten so far. What's throwing me off is the in the value of . I'm not sure how to handle this.