HW#1 - Due January 24th ECON 3102 1 Math Refresher (5 pts) Problems: (a) Find the derivative of f(x) = (In(x) )2 (b) Find the partial derivatives of f (x, y) = 5 + 2x3 + y + 4xdyl-a (c) Solve the following system of equations for x, y, and z: z + 2y = 2 - = 5 y x . y . z = 15 (d) A consumer has 10 dollars to spend on apples and bananas. The consumer's preferences can be repre- sented with the utility function u(a, b) = a . b, where a is the quantity of apples and b is the quantity of bananas. If apples cost 1 dollar each, and bananas cost 0.5 dollars each, how many of each fruit should the consumer buy to make themself as satisfied as possible with their purchase? Explain why