Homework 11

4 2 4 2 2 4 6 5 4 3 2 1 0 1 2 3 4 5 6 7 4 2 2 4

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Unformatted text preview: 2 3 4 5 6 7 4 2 2 4 -4 -2 2 4 3. 4 2 keywords: graph, vertical asymptote, horizontal asymptote, rational function 007 (part 1 of 1) 10 points 4. -4 -2 2 4 4 If f is a continuous function on (-4, 4) such that (i) f has 3 critical points, (ii) f has 1 local maximum, (iii) f (x) > 0 on (-4, -2), (iv) f (x) < 0 on (0, 2), (v) (0, 1) is an inflection point, (vi) f (x) < 0 on (2, 4), which one of the following could be the graph of f ? 1. 4 2 -4 -2 2 4 -4 -2 correct 6. 4 2 2 4 -4 -2 2 4 5. 4 2 -4 -2 2 4 2 Explanation: Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken Five of the graphs fail to have one or more of the 6 properties the graph of f has to have. Indeed, property (i) fails in 8 4 2 4 2 -4 -2 2 4 -4 -2 2 4 because (0, 1) is not an inflection point. On the other hand, the only remaining graph because the graph has only 2 critical points, while properties (i) and (ii) fail in 4 2 -4 -2 2 4 4 2 -4 -2 2 4 does have all six of the required properties. Consequently, this is a possible graph for f . because...
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This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

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