Homework 11

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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, y-intercept, 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 -6-5-4-3-2-10 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 -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 2 4 6 8 10 6 4 2 -4 -2 -2 -4 -6 -6-5-4-3-2-10 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.

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