(i) Find the extremal z* = **(t) for the functional J[w] = [. (52 + x2) dt, x(0) = 0, x(1) = 1. i.e. satisfying (1) (2* (t) = 2"(0) (ii) For the extremal *(t), you show that (2) [ 13"(0)] + [z"()?) dt = [ {**() #ce) + 2*(!) m(t) ] dt for all x = x(t) CT with x(0) = 0, x(1) = 1. (Hints: Multiplying equation (1) with n(t) = x*(t) - X(t) and then integration by parts.) (iii) You prove that x* = x*(t) is a minimizing curve, i.e. J[2*]