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Unformatted text preview: l maximum, concavity 009 (part 1 of 1) 10 points Explanation: Which function could have Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken while d sin x  dx 2 + cos x 2 =  cos x(2 + cos x)  sin2 x (2 + cos x)2 =  Thus as its graph on [ 0, 2]? 1. f (x) = 2. f (x) = sin x 2 + cos x sin x correct cos x  2 sin x 2 + cos x f (x) = sin x 2  cos x 2 cos x + 1 . (2 + cos x)2 10 has critical points when cos x = 1/2, i.e., at x = /3, 5/3, while f (x) = sin x 2 + cos x 3. f (x) =  4. f (x) = sin x 5. f (x) = sin x 2  cos x has critical points when cos x = 1/2, i.e., at x = 2/3, 4/3. Consequently, the graph can only be that of f (x) = sin x . cos x  2 6. f (x) =  sin x Explanation: As f (/2) < 0, this already eliminates the three choices for f in which f (/2) > 0, leaving only the possibilities sin x sin x ,  sin x ,  . cos x  2 2 + cos x To decide among these we check critical points because the graph has a local minimum in (0, /2) and a local maximum in (3/2, 2). Now  sin x has critical points at x = /2, 3/2, eliminating this...
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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.
 Spring '08
 schultz
 Differential Calculus

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