On the other hand the critical points of f occur when

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Unformatted text preview: he tangent line to the graph is horizontal, while the inflection points occur where the concavity changes sign. Consequently, if f is to have exactly two critical points and one inflection point its graph can only be 7 6 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 -1 0 1 2 3 4 5 6 7 8 9 1011 2 4 6 8 10 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 2 4 6 8 10 keywords: critical point, inflection point, graph, vertical asymptote 011 (part 1 of 1) 10 points 6 4 2 -4 -2 -2 -4 -6 2 4 6 8 10 correct A function f is continuous and twicedifferentiable for all x = 1. Its derivatives have the properties (i) f (-1) = 0, (ii) f (iii) f > 0 on (-, -2) < 0 on (-2, 1). (1, ), -6-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 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 If the lines x = 1 and y = 2 are asymptotes of the graph of f , which of the following could be the graph of f ? 7 6 6 1. 5 4 4 3 2 2 1 0 -1 -8 -6 -4 -2 2 4 6 -2 -2 -3 -4 -4 -5 -6 -6 -7 correct -9 -8 -7 -6...
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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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