I have a question that asks:
Find the extremal of the functional $$J(x)=\int^{\pi}_02x\sin(t)-\dot x^2 dt$$ with $x(0)=x(\pi)=0$. I found $x(t)=\sin(t)$
It then asks to
Show that this extremal provides the global maximum of $J$
I am not sure how to show this. Do I want to look at $J''(x)$ or at $x''(t)$