Given the function g(x) = 6x³ + 27x² 72x, find the first derivative, g'(x). g'(x) = 0 when x = -4, that is, Notice that g'(x) g'(4) = 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). g''(x) = Evaluate g''(-4). 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 = At x = - 4 the graph of g(x) is [Select an answer 4? Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at X = - 4? At x = 4 there is a local Select an answer ✓ - =

Given the function g(x) = 6x³ + 27x² 72x, find the first derivative, g'(x). g'(x) = 0 when x = -4, that is, Notice that g'(x) g'(4) = 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). g''(x) = Evaluate g''(-4). 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 = At x = - 4 the graph of g(x) is [Select an answer 4? Based on the concavity of g(x) at x = 4, does this mean that there is a local minimum or local maximum at X = - 4? At x = 4 there is a local Select an answer ✓ - =

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.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 37E

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