3 B (20 points) v(X) (1.0) X == A function () passes between the origin (x = 0, y = 0) and a point (x = 1, = 0) on the x-axis. We wish to minimize its mean square first derivative, F[v(x)] = *('(x)) dx, while fixing its mean square at a value of unity. (That is, we normalize it.) G[v(x)] = *(v(x)) dx = 1, and also fixing its end conditions (0) = (1) = 0. (4) (5) a) Introduce a global (independent of x) Lagrange undetermined multiplier A. Find the Euler equation that results from the corresponding compound functional F - XG. b) Solve the Euler equation from part a) and determine A. c) Show that (x) must be sinusoidal. (There are many stationary solutions (x); can you find them all? Only one of them corresponds to the minimum value of F. Others correspond merely to stationary values of F, and may be called saddle-points in the function space.)