Consider the following function and closed interval. f(x) = x2/3-7, [-27, 27] Is f continuous on the closed interval [-27,27]? Ⓒ Yes O No If f is differentiable on the open interval (-27, 27), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = DNE Find f(-27) and f(27). f(-27) = f(27) = X
Consider the following function and closed interval. f(x) = x2/3-7, [-27, 27] Is f continuous on the closed interval [-27,27]? Ⓒ Yes O No If f is differentiable on the open interval (-27, 27), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = DNE Find f(-27) and f(27). f(-27) = f(27) = X
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 35E
Related questions
Question
Find f(−27) and f(27).
![Consider the following function and closed interval.
f(x) = x²/3 – 7, [-27, 27]
Is f continuous on the closed interval [-27, 27]?
O Yes
Ο No
If f is differentiable on the open interval (-27, 27), find f'(x). (If it is not differentiable on the open interval, enter DNE.)
f'(x) = DNE
Find f(-27) and f(27).
f(-27) =
f(27)
=
X
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)
Yes, Rolle's Theorem can be applied.
No, because f is not continuous on the closed interval [a, b].
No, because f is not differentiable in the open interval (a, b).
No, because f(a) ‡ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
C = NA](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab6702de-5579-4c14-bacb-4d8e7e421acd%2F17f48062-8ccc-40b5-b600-6076233ac082%2Frzmwld_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following function and closed interval.
f(x) = x²/3 – 7, [-27, 27]
Is f continuous on the closed interval [-27, 27]?
O Yes
Ο No
If f is differentiable on the open interval (-27, 27), find f'(x). (If it is not differentiable on the open interval, enter DNE.)
f'(x) = DNE
Find f(-27) and f(27).
f(-27) =
f(27)
=
X
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)
Yes, Rolle's Theorem can be applied.
No, because f is not continuous on the closed interval [a, b].
No, because f is not differentiable in the open interval (a, b).
No, because f(a) ‡ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
C = NA
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