Consider the function f(x) = 4 – 6x² on the interval [- 2, 6]. Find the average or mean slope of the function on this interval, i.e. f(6) – f( – 2) 6 – (– 2) - By the Mean Value Theorem, we know there exists a c in the open interval (– 2, 6) 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) = 4 – 6x² on the interval [- 2, 6]. Find the average or mean slope of the function on this interval, i.e. f(6) – f( – 2) 6 – (– 2) - By the Mean Value Theorem, we know there exists a c in the open interval (– 2, 6) 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
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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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Consider the function.
![Consider the function f(x) = 4 – 6x on the interval
[- 2, 6]. Find the average or mean slope of the function
on this interval, i.e.
f(6) – f( – 2)
-
6 – ( – 2)
-
By the Mean Value Theorem, we know there exists a c in
the open interval (– 2, 6) such that f'(c) is equal to
this mean slope. For this problem, there is only one c that
works. Find it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1cb33a-5c09-4b39-b542-98ea2d958adc%2F30bd53bc-5282-4773-94ce-001b1be843f1%2Fw326lch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function f(x) = 4 – 6x on the interval
[- 2, 6]. Find the average or mean slope of the function
on this interval, i.e.
f(6) – f( – 2)
-
6 – ( – 2)
-
By the Mean Value Theorem, we know there exists a c in
the open interval (– 2, 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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