Question 5. (10 marks) (a) Find the derivative of f (x) = x2 - 2 and examine where the function is increasing or decreasing. (b) Use L'Hopital's Rule to find the following limits: (i) lime-0 1 (ii). limp-0 4 TH - y" (x > 0, y > 0) Question 6. (6 marks) .Find the elasticities of f(x) with respect to x (a) . f(x) = Ax, where A, b are constants with A # 0. (b) .f(a) = 4x2 (Hint: The elasticity of f(x) with respect to x is given by Elif(x) = Faf'(x)) Question 7. (8 marks) (a) Let f(x) = 212 Find f'(x) and find the maximum value of f on [0, co) and show that it is a maximum. (b) Using implicit differentiation Find the derivative of 1. y3 + 3x2y = 13 with respect to a and evaluate the derivative at x = 2 and y = 1 Question 8. (4 marks) Consider the following (piecewise defined) utility function : u(c) = 1 -p p# 1 In c p =1 Show that limp-19-= Inc Given this result, is u continuous at p = 1 ? Question 9. (6 marks) Suppose that the total cost of producing Q > 0 units of a commodity is C(Q) = aQ2 +bQ +c, where a, b, c are positive constants