Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that g'(x) 0 when x 4, that is, g' (4) = 0. %3D %3D %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). (x), ,6 Evaluate g''(4). %3D g''(4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 4? At x = 4 the graph of g(x) is Select an answer v %3D Based on the concavity of g(x) at x a local minimum or local maximum at x = 4? At x = 4 there is a local Select an answer v :4, does this mean that there is
Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that g'(x) 0 when x 4, that is, g' (4) = 0. %3D %3D %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). (x), ,6 Evaluate g''(4). %3D g''(4) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = 4? At x = 4 the graph of g(x) is Select an answer v %3D Based on the concavity of g(x) at x a local minimum or local maximum at x = 4? At x = 4 there is a local Select an answer v :4, does this mean that there is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Given the function g(x) = 8x + 12x - 480x, find the first
derivative, g'(x).
%3D
(x),6
Notice that g' (x) = 0 when a = 4, that is, g' (4)3 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).
%3D
Evaluate g''(4).
g''(4) =
%3D
Based on the sign of this number, does this mean the graph of g(x) is
concave up or concave down at x = 4?
At x = 4 the graph of g(x) is Select an answer v
Based on the concavity of g(x) at x = 4, does this mean that there is
a local minimum or local maximum at x
At x
4?
4 there is a local Select an answer v
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