Problem 3 (20 points). Part I (9 points) Find ALL local and global optimal solutions of the following minimization problems, whose objective function is denoted by f and feasible set by X (do NOT use Matlab or any other solver): (a). f(x) = sin x and X = [0, 3π]; (b). f(x) = sin x and X = [0, 4π]; (c). f(x) = sin x and X = [−π/4,(11/4)π]; (d). f(x) = max(0, x2 − 1) and X = (−[infinity], [infinity]); (e). f(x) = ( 1 x · sin (x), if x 6= 0 0, if x = 0; and X = [0,(2/3)π];