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Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x)= Notice that g'(x) = 0 when x = 3, that is, g'(3) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 3, so we will use the second derivative test. Find the second derivative, g''(x). _g''(x) = Evaluate g''(3). gʻʼ(3) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 3? At x = 3 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = 3, does this mean that there is a local minimum or local maximum at x = 3? At 3 there is a local Select an answer

Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x)= Notice that g'(x) = 0 when x = 3, that is, g'(3) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 3, so we will use the second derivative test. Find the second derivative, g''(x). _g''(x) = Evaluate g''(3). gʻʼ(3) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 3? At x = 3 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = 3, does this mean that there is a local minimum or local maximum at x = 3? At 3 there is a local Select an answer

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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Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x) = Notice that g'(x) = 0 when x = 3, that is, g'(3) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 3, so we will use the second derivative test. Find the second derivative, g''(x). g''(x) = Evaluate g''(3). g'' (3) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 3? At x = 3 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = 3, does this mean that there is a local minimum or local maximum at x = 3? At x=3 there is a local Select an answer
Transcribed Image Text:Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x) = Notice that g'(x) = 0 when x = 3, that is, g'(3) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 3, so we will use the second derivative test. Find the second derivative, g''(x). g''(x) = Evaluate g''(3). g'' (3) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 3? At x = 3 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = 3, does this mean that there is a local minimum or local maximum at x = 3? At x=3 there is a local Select an answer
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