Problem 4. Find the local minima, local maxima, and the saddle points for the functions: (a) Way) = 134 - 062/ + %y27 (b) g(:n,y) = x2 2x +y2 2y + 1. Problem 5. Let f(x,y) : 3:2 23: + y2 2y. (a) Find the local minima, local maxima, and the saddle points of f . (b) Sketch the region A 2 {(11:7 y)! :1: 2 0,1; 2 0, y g 3 711:}. (c) Find the absolute maximum and the absolute minimum of f on A. Problem 6. Find the absolute maximum and the absolute minimum of f(.7:,y) = m3+y33m on the region D = {(m,y)| 2 g :1: g 2, 2 S y S 2}. Problem 7. Find the absolute maximum and the absolute minimum of f(:1:, 1 ) = my + #12 011 the closed triangular region with vertices (0, 0), (2, 0), and (0, 2). Problem 8. Give an example of a function f of one variable and a value a such that f'(a) = f\"(a) = 0 and f has a local minimum at a