test1v2 - 1 2. Dene f ( x ) = x-1 x + 2 . (a) Determine the...

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M1020 Stream 2 Calculus Written Test 1 Semester 2, 2009 August 26, 2009 There are 2 questions worth a total of 9 marks 1 1. (a) A 216 m 2 rectangular field is to be enclosed by a fence and divided in two equal parts by another fence parallel to one of the other sides. Assuming that a minimum can be achieved, what dimensions of the outer rectangle will require the least amount of fence? How much fence will be needed? [3 marks] (b) Say why the global minimum can be achieved in part (a) above. [1 mark ] (c) Calculate lim x 0 x ln x . Show all working. [1 mark ] 1 Question 2 is on the next page.
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Unformatted text preview: 1 2. Dene f ( x ) = x-1 x + 2 . (a) Determine the domain of f , the derivative of f , and the critical points of f . Determine any points of local maximum and minimum, the intervals where f is increasing, and the intervals where f is decreasing. Find any horizontal or vertical asymtptotes of f . [2 marks] (b) Find the second derivative of f , the intervals where f is concave up, the intervals where f is concave down, and any points of inection. [1 mark ] (c) Use this information to sketch the graph of f . [1 mark ] 2...
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test1v2 - 1 2. Dene f ( x ) = x-1 x + 2 . (a) Determine the...

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