Given the function g(x) 4x³ - 30x² + 72x, 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? [Answer either up or down -- watch your spelling!!] At x = 3 the graph of g(x) is concave 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? [Answer either minimum or maximum -- watch your spelling!!] At x = 3 there is a local
Given the function g(x) 4x³ - 30x² + 72x, 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? [Answer either up or down -- watch your spelling!!] At x = 3 the graph of g(x) is concave 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? [Answer either minimum or maximum -- watch your spelling!!] At x = 3 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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![Given the function g(x) = 4x³
g'(x)
=
Notice that g'(x)
=
Evaluate g"(3).
g″(3) =
=
0 when x =
30x² + 72x, find the first derivative, g'(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) =
Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at
X = = 3?
[Answer either up or down watch your spelling!!]
At x = 3 the graph of g(x) is concave
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?
[Answer either minimum or maximum -- watch your spelling!!]
At x = 3 there is a local](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaa5e485-2140-4422-9ef2-b97627b78924%2Fde96f856-1d3f-4521-816a-70e0c4c1288c%2Fni5ou3_processed.png&w=3840&q=75)
Transcribed Image Text:Given the function g(x) = 4x³
g'(x)
=
Notice that g'(x)
=
Evaluate g"(3).
g″(3) =
=
0 when x =
30x² + 72x, find the first derivative, g'(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) =
Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at
X = = 3?
[Answer either up or down watch your spelling!!]
At x = 3 the graph of g(x) is concave
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?
[Answer either minimum or maximum -- watch your spelling!!]
At x = 3 there is a local
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