Find the derivative of the given function. f(x) = (2x² + 2)³(x² - 1)² f'(x) 80x⁹ +64x7 - 96x5 − 64x³ + 16x What is the domain of f(x)? Ⓒ (-∞, ∞) [1, ∞) O [-1, 1] O (0, ∞) = What is the domain of f '(x)? O [1, ∞) O [-1, 1] O (-∞, -1) ● (-∞0, ∞0) (0, ∞) X = Find all x-values at which the function has horizontal tange -1 (smallest value) X = X = (-∞, -1) X = X = 이 sqrt((−1+sqrt(5))/4) -sqrt(( − 1 + sqrt(5))/4) -1 X (largest value)
Find the derivative of the given function. f(x) = (2x² + 2)³(x² - 1)² f'(x) 80x⁹ +64x7 - 96x5 − 64x³ + 16x What is the domain of f(x)? Ⓒ (-∞, ∞) [1, ∞) O [-1, 1] O (0, ∞) = What is the domain of f '(x)? O [1, ∞) O [-1, 1] O (-∞, -1) ● (-∞0, ∞0) (0, ∞) X = Find all x-values at which the function has horizontal tange -1 (smallest value) X = X = (-∞, -1) X = X = 이 sqrt((−1+sqrt(5))/4) -sqrt(( − 1 + sqrt(5))/4) -1 X (largest value)
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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Do the last part
![Find the derivative of the given function.
f(x) = (2x² + 2)³(x² - 1)²
80x⁹ +64x7 - 96x5 – 64x³ + 16x
f'(x)
What is the domain of f(x)?
Ⓒ (-∞, ∞)
[1, ∞)
O [-1, 1]
=
O (0, ∞)
What is the domain of f '(x)?
O [1, ∞)
O [-1, 1]
O (-∞, -1)
● (-∞, ∞)
O (0, ∞)
(-∞, -1)
Find all x-values at which the function has horizontal tangent lines. (If an answer does not exist, enter DNE.)
x= -1
(smallest value)
X =
X = 0
X =
X =
sqrt(( − 1 +sqrt(5))/4)
-sqrt((−1+sqrt(5))/4)
-1
(largest value)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2e4bb04-cee2-49bd-b671-fd8e923933f3%2Fbb603a21-0c81-4791-b7f6-e50e506eaa80%2Fj13qgsk_processed.png&w=3840&q=75)
Transcribed Image Text:Find the derivative of the given function.
f(x) = (2x² + 2)³(x² - 1)²
80x⁹ +64x7 - 96x5 – 64x³ + 16x
f'(x)
What is the domain of f(x)?
Ⓒ (-∞, ∞)
[1, ∞)
O [-1, 1]
=
O (0, ∞)
What is the domain of f '(x)?
O [1, ∞)
O [-1, 1]
O (-∞, -1)
● (-∞, ∞)
O (0, ∞)
(-∞, -1)
Find all x-values at which the function has horizontal tangent lines. (If an answer does not exist, enter DNE.)
x= -1
(smallest value)
X =
X = 0
X =
X =
sqrt(( − 1 +sqrt(5))/4)
-sqrt((−1+sqrt(5))/4)
-1
(largest value)
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