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Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x) = 0 when x 4, that is, g'(4) = 0. %3D Now, we want to know whether there is a local minimum or local maximum at x= 4, so we will use the second derivative test. Find the second derivative, g"(x). g"(x) = Evaluate g"(4). g"(4) = Based on the sign of this number, does this mean the graph of g(x) concave down at x = 4? [Answer either up or down -- watch your spelling!!] concave up or At x = 4 the graph of g(x) is concave Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at x = [Answer either minimum or maximum -- watch your spelling!!] 4? At x = 4 there is a local

Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x) = 0 when x 4, that is, g'(4) = 0. %3D Now, we want to know whether there is a local minimum or local maximum at x= 4, so we will use the second derivative test. Find the second derivative, g"(x). g"(x) = Evaluate g"(4). g"(4) = Based on the sign of this number, does this mean the graph of g(x) concave down at x = 4? [Answer either up or down -- watch your spelling!!] concave up or At x = 4 the graph of g(x) is concave Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at x = [Answer either minimum or maximum -- watch your spelling!!] 4? At x = 4 there is a local

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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3 Given the function g(x) = 6x° – 27x? – 72x, find the first derivative, g'(x). (x),6 Notice that (x),6 O when x = 4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 4, so we will use the second derivative test. Find the second derivative, g"(x). g"(x) = Evaluate g"(4). g"(4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or 4? concave down at x = [Answer either up or down At x = 4 the graph of g(x) is concave watch your spelling!!] Based on the concavity of g(x) at x = :4, does this mean that there is a local minimum or local maximum at x = 4? [Answer either minimum or maximum watch your spelling!!] At x = 4 there is a local
Transcribed Image Text:3 Given the function g(x) = 6x° – 27x? – 72x, find the first derivative, g'(x). (x),6 Notice that (x),6 O when x = 4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at x = 4, so we will use the second derivative test. Find the second derivative, g"(x). g"(x) = Evaluate g"(4). g"(4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or 4? concave down at x = [Answer either up or down At x = 4 the graph of g(x) is concave watch your spelling!!] Based on the concavity of g(x) at x = :4, does this mean that there is a local minimum or local maximum at x = 4? [Answer either minimum or maximum watch your spelling!!] At x = 4 there is a local
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