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Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that g'(x) = 0 when a = 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). = (ɛ),,6 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 I = 3 the graph of g(x) is Select an answer v 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 v

Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that g'(x) = 0 when a = 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). = (ɛ),,6 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 I = 3 the graph of g(x) is Select an answer v 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 v

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
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Given the function g(x) = 4x° + 12x? 180x, find the first derivative, g'(x). = (x),6 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 v 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 v
Transcribed Image Text:Given the function g(x) = 4x° + 12x? 180x, find the first derivative, g'(x). = (x),6 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 v 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 v
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