( marks) [Question 31 Given the curve f(x) = x'-12.x2 +36x : Find the coordinates of the stationary points and determine the nature of them. (6 marks) [Question 4] Given that the demand function for a monopolist's product is p = 2x2 +10x +1000 and the 20 average-cost function is C' = 2.x2 + 36x -1600- , where x is number of units, and both p and X C are expressed in dollars per unit. i. Determine the level output at which profit is maximized. (4 marks) ii. Determine price at which maximum profit occurs. (4+ marks) iii. Determine the maximum profit. (2 marks)MTH2129 (UNIT 2) WORKSHEET [Question 5] If the average-cost function for a manufacturer is given by C = 4x-10+ 7000 X where q is the number of pens manufactured and C is expressed in dollars per pen. (a) Find the marginal-cost function. (3 marks) ( b ) Find the marginal cost when x =20 and interpret your result