Consider a function f : R R defined as f(x) = x55x3+22x + 30x +36 (a) Find the first derivative, f'(x), and the second derivative, f" (x), of the function f and verify that they are well-defined and continuous at x = = 0. (b) Find all critical points of and classify them into local max, local min, and inflection points. (c) Find all global max points of if exist(s). Find all global min points of if exist(s). (d) Find all solutions to the following problem: max f(xy) (x,y)ER2 (xy)5+5(xy)3 + 22(xy) + 30(xy) + 36 = s.t. x + y = 22. (e) Find the solution to the following problem: min ln(x + y) + (x,y)R xy s.t. h(x,y) = (x 1.5) + (y 1.5) 2 1 0.