QUESTION 4 (4.1) Find the extremal (if it exists) of the isoperimetric problem with the functional (14) I [x] = (ic2 - +2 ) dt, subject to the conditions x dt = 1, x (0) = 0, x(2) = 2. (4.2) Consider the variational problem with Lagrangian function (6) L (t, x, ic) = 32 - 2xt and endpoint conditions x(0) = 0, x(1) = -2. Show that the Weierstrass Excess function is positive. [20]