Solve and explain questions 1 and 2

Moppe 2 ANSWER ALL QUESTIONS 1) a) Differentiate the following with respect to x (Simplify your answers) i. f (x ) = 3x4 - 7Vx+ 3+2 [2 MARKS] ii. f (x) = (3-5x) 4 [3 MARKS] y = 2xe3-2x [3 MARKS] iv. y = " In (2x) 6x3 [4 MARKS] b) i) Find the values of x at the turning points of the function f(x) =x3-3x2+2 [6 MARKS] ii) Classify the turning points determined above. [4 MARKS] c) Determine all second-order partial derivatives of the following function. z = 4x2y2 + 7x -3y+2 [4 MARKS] A firm's revenue function and cost function for an item x are given by: Cost function C(x) = 5000 + 20x Revenue function R(x) = 100x - 0.2x2 a) Derive the profit function P(x) In terms of x. [2 MARKS] b) Derive the marginal profit P'(x) in terms of x. [2 MARKS] c) Calculate the marginal profit when x = 100 [2 MARKS] d) Determine the value of x that maximises profit. (Verify that the value obtained is a maximum) [4 MARKS] e) State the maximum profit of the firm. [2 MARKS] PLEASE TURN OVER