Need help with microecon

Suppose a consumer values consumption (C) and leisure (Z) according to the utility function we, Z) = 01/2 +an (a) Are the marginal utilities for consumption and the marginal utility of leisure always positive or always negative? Demonstrate mathematically. (b) Does this utility function exhibit diminishing marginal utility for both consumption and leisure? Demonstrate mathematically. (c) We can rewrite the utility function in terms of labor H = 1 Z. U(C, H) = U(C) V(H) = 01/2 [ ln(l H)] \\v"' V(H): disutility of labor Is the marginal disutility of labor always positive or negative? Does this utility function exhibit diminishing marginal disutility for labor