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Consider the function f(x) =1– 7x on the interval [ – 4, 4]. Find the average or mean slope of the function on this interval, i.e. f(4) – f( – 4) 4 - (– 4) By the Mean Value Theorem, we know there exists a c in the open interval ( – 4, 4) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Consider the function f(x) =1– 7x on the interval [ – 4, 4]. Find the average or mean slope of the function on this interval, i.e. f(4) – f( – 4) 4 - (– 4) By the Mean Value Theorem, we know there exists a c in the open interval ( – 4, 4) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Calculus For The Life Sciences
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.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Consider the function f(x) = 1 – 7x? on the interval [ – 4, 4]. Find the average or mean slope of the function on this interval, i.e. f(4) – f( – 4) 4 – (– 4) By the Mean Value Theorem, we know there exists a c in the open interval (- 4, 4) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
Transcribed Image Text:Consider the function f(x) = 1 – 7x? on the interval [ – 4, 4]. Find the average or mean slope of the function on this interval, i.e. f(4) – f( – 4) 4 – (– 4) By the Mean Value Theorem, we know there exists a c in the open interval (- 4, 4) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
Consider the function f(x) on the interval [1, 6]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1, 6) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
Transcribed Image Text:Consider the function f(x) on the interval [1, 6]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (1, 6) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
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