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Tutorial Exercise Find the inflection point(s), if any, of the function. 9g(x) = 6x³9x² + 4x - 9

Tutorial Exercise Find the inflection point(s), if any, of the function. 9g(x) = 6x³9x² + 4x - 9

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Tutorial Exercise Find the inflection point(s), if any, of the function. g(x) = 6x³9x² + 4x - 9 Step 1 Recall that an inflection point is a point on the graph of a continuous function where the tangent line exists and where the concavity changes. To find inflection points for the given function, we follow the method below. 1. Compute g"(x). 2. Determine the numbers in the domain of g for which g"(x) = 0 or g"(x) does not exist. 3. Determine the sign of g"(x) to the left and right of each number c found in Step 2. If there is a change in the sign of g"(x) as we move across x = c, then (c, f(c)) is an inflection point of g. We first compute g"(x). g(x) = 6x³9x² + 4x - 9 g'(x) = g"(x) = Submit x2 18x + 4 - 18 Skip (you cannot come back)
Transcribed Image Text:Tutorial Exercise Find the inflection point(s), if any, of the function. g(x) = 6x³9x² + 4x - 9 Step 1 Recall that an inflection point is a point on the graph of a continuous function where the tangent line exists and where the concavity changes. To find inflection points for the given function, we follow the method below. 1. Compute g"(x). 2. Determine the numbers in the domain of g for which g"(x) = 0 or g"(x) does not exist. 3. Determine the sign of g"(x) to the left and right of each number c found in Step 2. If there is a change in the sign of g"(x) as we move across x = c, then (c, f(c)) is an inflection point of g. We first compute g"(x). g(x) = 6x³9x² + 4x - 9 g'(x) = g"(x) = Submit x2 18x + 4 - 18 Skip (you cannot come back)
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