104/184 Quiz #3 - P3
October 22/23
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Last Name:
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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: