Given the function g(x) = 4x + 30x + 48x, find thefirst derivative, g'(x).g'(x) =Notice that g'(x) =O when x =- 1, that is,g'( – 1) = 0.Now, we want to know whether there is a local minimum or– 1, so we will use the secondlocal maximum at x =derivative test.Find the second derivative, g''(x).g''(x)Evaluate g''( - 1).g''( – 1) =Based on the sign of this number, does this mean the graph- 1?watch your spelling!!]of g(x) is concave up or concave down at x =[Answer either up or downAt x1 the graph of g(x) is concaveBased on the concavity of g(x) at x =mean that there is a local minimum or local maximum at- 1, does thisr = -1?watch your[Answer either minimum or maximumspelling!!]--At x =1 there is a local

Answered: Image /qna-images/answer/89c225c7-6008-495a-b7aa-af5d58f3929f.jpg

Given the function g(x) = 4x° + 30x2 + 48x, find the first derivative, g'(x). gʻ(x) = Notice that g'(x) O when x = - 1, that is, %3D g'( – 1) = 0. Now, we want to know whether there is a local minimum or - 1, so we will use the second local maximum at x = derivative test. Find the second derivative, g''(x). = (x),,6 Evaluate g''( - 1). g''(– 1) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at a = [Answer either up or down -- watch your spelling!!] - 1 the graph of g(x) is concave 1? At x = Based on the concavity of g(x) at x = mean that there is a local minimum or local maximum at 1, does this x = 1? [Answer either minimum or maximum -- watch your spelling!!] At x = – 1 there is a local

Given the function g(x) = 4x° + 30x2 + 48x, find the first derivative, g'(x). gʻ(x) = Notice that g'(x) O when x = - 1, that is, %3D g'( – 1) = 0. Now, we want to know whether there is a local minimum or - 1, so we will use the second local maximum at x = derivative test. Find the second derivative, g''(x). = (x),,6 Evaluate g''( - 1). g''(– 1) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at a = [Answer either up or down -- watch your spelling!!] - 1 the graph of g(x) is concave 1? At x = Based on the concavity of g(x) at x = mean that there is a local minimum or local maximum at 1, does this x = 1? [Answer either minimum or maximum -- watch your spelling!!] At x = – 1 there is a local

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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