Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number € (0, 2) such that (2x)-f(0) 2-0 = f'(5). Round the value of to 2 decimals. Answer:

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
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Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number
E € (0, 2) such that
f(2x)-f(0)
2x-0
= f'(§).
Round the value of to 2 decimals.
Answer:
Transcribed Image Text:Consider the function f(x) = x + sin(2x) defined on the interval [0, 2x]. Verify that the mean value theorem holds for the function on the given interval. In other words, show that there exists a number E € (0, 2) such that f(2x)-f(0) 2x-0 = f'(§). Round the value of to 2 decimals. Answer:
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