Could you help me solve these 2 problems about intermediate microeconomics?

3. a.) Dene what is meant by a monotonic transformation of some consumer's utility function: u (:31, 222). b) Suppose u(a:1, $2) = 3:121 + 2x2. Sketch indifference curves for this consumer corresponding to utility levels 10, 20 and 30. c) Suppose u (2:1, :62) = $1 + $2. Sketch indifference curves for this consumers corresponding to utility levels 10, 20 and 30. (1) Can these two utility functions be said to describe the same preferences: Is the function in b) a monotonic transformation of the function in c). Explain. (25 pts) 1 1 4. Suppose an individual has a utility function u(:c1,x2) = 41:12:32\". Present your mathmatical expressions below in the simplest form you can. a) Derive an expression for the marginal utility of good 1, and for the marginal utility of good 2. b) Using these. solve for an expression describing the slope of an indifference curve: M RS (:31, 3:2). 1 1 c) Sketch indifference curves for this consumer corresponding to u = 0, 10, 20. (Hint: at? z; = k I 1 solves for 3-25 = k/ (x12) .... Solve this expression and approximate it on a graph for the three values of k..)(25 pts)