Given the function g(æ) = 6a³ + 9x² – 36x, find the first derivative, g'(x). g'(x) = Preview Notice that g'(x) = 0 when a = – 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at æ = – 2, so we will use the second derivative test. Find the second derivative, g''(x). 9'"(x) = Preview Evaluate g''( – 2). 9'"(– 2) =

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Given the function g(æ) = 6x³ + 9x² – 36, find the first derivative, g'(æ).
g'(x) =
Preview
Notice that g'(x) = 0 when æ
- 2, that is, g'( – 2) = 0.
Now, we want to know whether there is a local minimum or local maximum at æ = – 2, so we will use the second
derivative test.
Find the second derivative, g''(x).
g'"(x) =
Preview
Evaluate g''( – 2).
g''( – 2) =
Based on the sign of this number, does this mean the graph of g(æ) is concave up or concave down at æ = – 2?
At x = - 2 the graph of g(x) is Select an answer ♥
- 2, does this mean that there is a local minimum or local maximum at
Based on the concavity of g(x) at æ
= - 2?
At æ = - 2 there is a local Select an answer v
%3D
Transcribed Image Text:Given the function g(æ) = 6x³ + 9x² – 36, find the first derivative, g'(æ). g'(x) = Preview Notice that g'(x) = 0 when æ - 2, that is, g'( – 2) = 0. Now, we want to know whether there is a local minimum or local maximum at æ = – 2, so we will use the second derivative test. Find the second derivative, g''(x). g'"(x) = Preview Evaluate g''( – 2). g''( – 2) = Based on the sign of this number, does this mean the graph of g(æ) is concave up or concave down at æ = – 2? At x = - 2 the graph of g(x) is Select an answer ♥ - 2, does this mean that there is a local minimum or local maximum at Based on the concavity of g(x) at æ = - 2? At æ = - 2 there is a local Select an answer v %3D
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