For each of the following functions use the test given in Appendix 2 to determine whether it is convex, concave, or neither. Also, find the local minimum, local maximum, and saddle points of each function. If you can conclude the local minimum/maximum are global minimum/maximum, please Show them. (a) f(x) = x_1 x_ 2 - x^2_1 x^2_2 (b) f(x) = 3x_1+ 2x^2_1 + 4x_2 + x^2_2 - 2x_1 x_2 (c) f (x) = x^2_1 + 3x_1 x_2 + 2x^2_2 (d) f(x) = 20 x_1 + 10 x_2 (e) f(x) = x_1 x_2