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practice test 3 1009

# practice test 3 1009 - f is concave upward and concave...

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1 Carleton University School of Mathematics and Statistics Math 1009 – Calculus – Practice Test #3 of 4 NAME: __________________________________ STUDENT NUMBER: __________________________ INSTRUCTIONS : There are TWO written questions. Each question outlines its own marking scheme. Please read each question carefully. For full marks, be sure to show all of your work and justify all of your steps . 1. Consider the function 1 1 ) ( + = x x x f . Answer the following questions. (A) ( 1 mark ) What is the domain of f ? (B) ( 3 marks ) Find the x – and y – intercepts of f .

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2 (C) ( 4 marks ) Find the vertical and horizontal asymptotes of f .
3 (D) ( 5 marks ) Determine the intervals of increase and decrease of f . Explain why f has no relative extrema.

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4 (E) ( 5 marks ) Determine the intervals where

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Unformatted text preview: f is concave upward and concave downward. Despite the fact that there is a value of x over which f changes concavity, explain why f does not have an inflection point. 5 (F) ( 4 marks ) Sketch the graph of f making use of your results from parts (A) through (E). Plot additional points as needed. 6 2. ( 4 marks ) The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of it’s model M1 camera is , 10000 240 04 . ) ( 2 ≥ − + − = x x x x P . To maximize its profits, how many cameras should Cannon produce each month? Use the Second Derivative Test to verify that the value of x you obtain corresponds to the absolute maximum....
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practice test 3 1009 - f is concave upward and concave...

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