104/184 Quiz #3 - P3 October 22/23 First Name: Last Name: Student-No: Section: Grade: Very short answer questions 1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes. 3 x (a) Differentiate ln x e Answer: (b) Differentiate cos √ x Answer: Short answer questions — you must show your work 2. 4 marks Each part is worth 2 marks. (a) The position of an object moving horizonatally after t is given by f (t) = t2 + 3t Find its average velocity over the interval t = 1 to t = 3 seconds. Answer: (b) Determine the slope of xy + x3/2 y −1/2 = 2 at the point (1, 1). Answer: Long answer question — you must show your work 3. 4 marks Suppose that the total cost of producing x aroma diffusers is given by C(x) = 1500 + 10x + 0.04x2 (a) Find the average cost of producing 500 diffusers. Answer: (b) Estimate the cost of producing 501st diffuser. Answer: (c) Without computing the actual cost of the 501st diffuser, is the answer from part (b) an overestimate or underestimate? Explain your reasoning. Answer: