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Given the function g(x) = 8x³ + 12² – 48x, find the first derivative, g' (x). g'(x) = Notice that g'(x) = 0 when æ = - 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at æ = - 2, so we will use the second derivative test. Find the second derivative, g''(x). 9'"(x) = Evaluate g''( – 2). 9'"(- 2) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at a = - 2? At æ = - 2 the graph of g(æ) is Select an answer ♥ - 2, does this mean that there is a local minimum or local Based on the concavity of g(x) at æ maximum at a = - 2? At a = - 2 there is a local Select an answer Question Help: D Video OMessage instructor

Given the function g(x) = 8x³ + 12² – 48x, find the first derivative, g' (x). g'(x) = Notice that g'(x) = 0 when æ = - 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at æ = - 2, so we will use the second derivative test. Find the second derivative, g''(x). 9'"(x) = Evaluate g''( – 2). 9'"(- 2) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at a = - 2? At æ = - 2 the graph of g(æ) is Select an answer ♥ - 2, does this mean that there is a local minimum or local Based on the concavity of g(x) at æ maximum at a = - 2? At a = - 2 there is a local Select an answer Question Help: D Video OMessage instructor

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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Question 14 > Given the function g(x) = 8x3 + 12a? – 48x, find the first derivative, g' (x). g'(x) = Notice that g' (x) = 0 when a = - 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at z = - 2, so we will use the second derivative test. Find the second derivative, g'" (x). g'"(x) = Evaluate g''( – 2). g'"(– 2) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at z = – 2? At r = - 2 the graph of g(x) is Select an answer - 2, does this mean that there is a local minimum or local Based on the concavity of g(x) at a = maximum at æ = - 2? At a = - 2 there is a local Select an answer v Question Help: DVideo MMessage instructor Submit Question
Transcribed Image Text:Question 14 > Given the function g(x) = 8x3 + 12a? – 48x, find the first derivative, g' (x). g'(x) = Notice that g' (x) = 0 when a = - 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at z = - 2, so we will use the second derivative test. Find the second derivative, g'" (x). g'"(x) = Evaluate g''( – 2). g'"(– 2) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at z = – 2? At r = - 2 the graph of g(x) is Select an answer - 2, does this mean that there is a local minimum or local Based on the concavity of g(x) at a = maximum at æ = - 2? At a = - 2 there is a local Select an answer v Question Help: DVideo MMessage instructor Submit Question
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