Given the function g(x) = 8x³ + 12x² derivative, g'(x). g'(x) = Notice that g'(x) is, g'(- 4) = 0. = 288x, find the first 0 when x = 4, that 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) =
Given the function g(x) = 8x³ + 12x² derivative, g'(x). g'(x) = Notice that g'(x) is, g'(- 4) = 0. = 288x, find the first 0 when x = 4, that 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) =
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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Transcribed Image Text:Given the function
g(x) = 8x³ + 12x²
derivative, g'(x).
g'(x) =
Notice that g'(x)
is, g'(- 4) = 0.
=
=
Evaluate g''(- 4).
g''( — 4)
=
288x, find the first
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)
0 when x =
4, that
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