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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
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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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
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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