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Unformatted text preview: choice. On the other hand, by the Quotient Rule, d sin x dx cos x  2 cos x(cos x  2) + sin2 x = (cos x  2)2 = 1  2 cos x , (cos x  2)2 keywords: graph, trig function, local extrema, yintercept, 010 (part 1 of 1) 10 points A function f is continuous and twicedifferentiable for all x except x = 3, 2. If its graph has exactly two critical points and one inflection point, which of the following could be the graph of f ?
7 6 1.5 4 3 2 1 0 1 2 3 4 5 6 7 6 4 2 4 2 2 4 6
6543210 1 2 3 4 5 6 7 8 9 10 11 2 4 6 8 10 Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken
7 6 2.5 4 3 2 1 0 1 2 3 4 5 6 7 7 6 3.5 4 3 2 1 0 1 2 3 4 5 6 7 7 6 4.5 4 3 2 1 0 1 2 3 4 5 6 7 7 6 5.5 4 3 2 1 0 1 2 3 4 5 6 7 7 6 6.5 4 3 2 1 0 1 2 3 4 5 6 7 11 6 4 2 4 2 2 4 6
6543210 1 2 3 4 5 6 7 8 9 10 11 2 4 6 8 10 6 4 2 4 2 2 4 6
6543210 1 2 3 4 5 6 7 8 9 10 11 Explanation: If f is differentiable everywhere except at x = 3, 2, then already 3 of the graphs can be eliminated since these have vertical asymptotes at x = 2, 3. On the other hand, the critical points of f occur when f (x) = 0, i.e., when t...
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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.
 Spring '08
 schultz
 Differential Calculus

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