What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) f'(x) = (x - 1)²(x + 2) f'(x) = (x − 1)(x + 2)(x − 3)
What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) f'(x) = (x - 1)²(x + 2) f'(x) = (x − 1)(x + 2)(x − 3)
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Question
![8. Answer the following questions about the functions whose derivatives are given
below.
i.
ii.
111.
What are the critical points of f?
On what open intervals is f increasing or decreasing?
At what points, if any, does f assume local maximum and minimum values?
f'(x) = x(x - 1)
a.
b. f'(x) = (x-1)² (x + 2)
c. f'(x) = (x − 1)(x + 2)(x − 3)
x² (x-1)
d. f'(x)
x+2
O
e. f'(x) = 1 -
-, x = -2
4
x2 x 0
f. f'(x) = x−¹/³ (x + 2)
1/3,
g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40691494-888b-4a7b-8bd4-14b23ab3af57%2F98e1f0b7-01f0-4741-87b5-72b296eaf6a3%2Fylxf27f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Answer the following questions about the functions whose derivatives are given
below.
i.
ii.
111.
What are the critical points of f?
On what open intervals is f increasing or decreasing?
At what points, if any, does f assume local maximum and minimum values?
f'(x) = x(x - 1)
a.
b. f'(x) = (x-1)² (x + 2)
c. f'(x) = (x − 1)(x + 2)(x − 3)
x² (x-1)
d. f'(x)
x+2
O
e. f'(x) = 1 -
-, x = -2
4
x2 x 0
f. f'(x) = x−¹/³ (x + 2)
1/3,
g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π
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Follow-up Questions
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Follow-up Question
![8. Answer the following questions about the functions whose derivatives are given
below.
i.
ii.
iii.
What are the critical points of f ?
On what open intervals is f increasing or decreasing?
At what points, if any, does f assume local maximum and minimum values?
d. f'(x) =
e. f'(x) =
-
x²(x-1)
x+2
4
1 - x = 0
x2,
)
x = -2
f. f'(x) = x-¹/³ (x + 2)
-1/3
g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π
-](https://content.bartleby.com/qna-images/question/40691494-888b-4a7b-8bd4-14b23ab3af57/47282ffb-a6c4-46f9-9b0e-0510bd96c9bb/2on74v8_thumbnail.jpeg)
Transcribed Image Text:8. Answer the following questions about the functions whose derivatives are given
below.
i.
ii.
iii.
What are the critical points of f ?
On what open intervals is f increasing or decreasing?
At what points, if any, does f assume local maximum and minimum values?
d. f'(x) =
e. f'(x) =
-
x²(x-1)
x+2
4
1 - x = 0
x2,
)
x = -2
f. f'(x) = x-¹/³ (x + 2)
-1/3
g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π
-
Solution
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