Q5. In this question, you will play around with the possible derivatives of C2 functions f : R2 - R. (a) Can there exist a C2-function f such that the following holds? f= = 2x - 5y fy = 4x+ y If there can exist such a function, give an example of one. If there cannot exist such a function, explain why not. (b) Can there exist a C2-function f such that the following holds? fx = 2x - 5y fy =-5x +2 If there can exist such a function, give an example of one. If there cannot exist such a function, explain why not. (c) Clearly state a necessary condition for the existence of a C2- function with fa = 91(r, y) and fy = 92(I, y)