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Question 5 - 22 marks Let a 0 for all x E [a, b). (a) Let A > 0, B > 0 be constants. Show that the stationary path of the functional Styl = def(x) v1+y/, y(a) = A, y(b) = B. is given by y(z) = At8/ dw where 8 is a constant satisfying B AB du V/(w)2 - 32 (b*) Using the Jacobi equation, show that the stationary path found in part (a) gives a weak local minimum of the functional Sly]. (You are not required to solve the Jacobi equation.) (c*) Using the inequality (which is valid for all real z and w) VI+ (z+ 1)? v1+z2 2 1+2 or otherwise, show that the stationary path found in part (a) gives a global minimum of the functional Sly]