Let f(x) = (x - 3)-2. Find all values of c in (2, 5) such that f(5) – f(2) = f'(c)(5 – 2). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C = Based off of this information, what conclusions can be made about the Mean Value Theorem? O This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (2, 5) such that f'(c) = 15) - 12). 3D O This does not contradict the Mean Value Theorem since f is not continuous at x = 3. O This does not contradict the Mean Value Theorem since f is continuous on (2, 5), and there exists a c on (2, 5) such that f'(c) = 16) - (2). 5 - 2 O This contradicts the Mean Value Theorem since there exists a c on (2, 5) such that f'(c) = 5=R2), but f is not continuous at x = 3.
Let f(x) = (x - 3)-2. Find all values of c in (2, 5) such that f(5) – f(2) = f'(c)(5 – 2). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C = Based off of this information, what conclusions can be made about the Mean Value Theorem? O This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (2, 5) such that f'(c) = 15) - 12). 3D O This does not contradict the Mean Value Theorem since f is not continuous at x = 3. O This does not contradict the Mean Value Theorem since f is continuous on (2, 5), and there exists a c on (2, 5) such that f'(c) = 16) - (2). 5 - 2 O This contradicts the Mean Value Theorem since there exists a c on (2, 5) such that f'(c) = 5=R2), but f is not continuous at x = 3.
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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Transcribed Image Text:Let f(x) = (x – 3)-2. Find all values of c in (2, 5) such that f(5) – f(2) = f'(c)(5 – 2). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
C =
Based off of this information, what conclusions can be made about the Mean Value Theorem?
O This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (2, 5) such that f'(c)
f(5) – f(2)
5 - 2
%3D
O This does not contradict the Mean Value Theorem since f is not continuous at x = 3.
f(5) – f(2)
5 - 2
O This does not contradict the Mean Value Theorem since f is continuous on (2, 5), and there exists a c on (2, 5) such that f'(c) =
O This contradicts the Mean Value Theorem since there exists a c on (2, 5) such that f'(c) =
f(5) – f(2)
5 - 2
but f is not continuous at x = 3.
O Nothing can be concluded.
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