Please solve all, super confused. Thank you!

1. (35 points). The following utility functions are functions of the non-negative quantities consumed of the two goods, x, and x, . For each of them, can the implicit function theorem be used to find the marginal rate of substitution (the MRS is the steepness of an indifference curve)? At all consumption bundles or just some? If it cannot, show why. If it can, explain why and find the marginal rate of substitution using the implicit function rule. a) U(x,x, ) = x x, where a > 0 and B > 0. b) U (x, , x, ) = ax, + Bx, where a > 0 and B> 0. c) u(x,, x, ) = min {ax , Bx, where a > 0 and B> 0