Homework 11

# On the other hand the critical points of f occur when

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online