Find and classify all the critical points of the function f(x, y) = sin(x + y) - cost on the square S = [-1, 7] x [-1,7], i.e. S= {(x, y) ER?| -1 cos(x +y) = 0 =>aty= = (choose one of the following)) (i) nx/2 ii) 3nx/2 (iii) (2n + 1)7/2 (iv) -n7/2, where n E Z. This implies y = (choose one of the following)) (i) nn/2 - 2 (ii) nw/2 - I (iii) (2n + 1)7/2-1 (iv) -nn/2 - x, where n E Z. Thus, the critical points of f in all of IR2 are given by fx =0 >= , meZ, and y = (2n+ 1)7 - ma = ]+| keZ follows. From the critical points of f in IR, we need to select those which lie in the square S. These points are exactly given by the following choices of m and k: m =0, 1, 2, and k = 0, 1; that is (Write: 37 /2 as 3pi/2, do not use *) Pi(m = 0, k =0) = P2(m = 0, k = 1) = P3(m = 1, k =0) = PA(m = 1, k = 1) = Ps(m = 2, k = 0) = P6(m = 2, k = 1) = These critical points are of the following types Classification Critical point fir D Classification PI P2 saddle min P3 max