= Consider the function f(x) 2 - 2x² on the interval [2, 3]. Find the average or mean slope of the function on this interval, i.e. ƒ(3) – f(− 2) 3- (-2) = By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 3) such that ƒ'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 7T
Question
Consider the function f(x) = 2 – 2x² on the interval [ – 2, 3]. Find the average or mean slope of the
function on this interval, i.e.
ƒ(3) – ƒ( − 2)
3 − ( − 2)
By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 3) such that ƒ'(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) = 2 – 2x² on the interval [ – 2, 3]. Find the average or mean slope of the function on this interval, i.e. ƒ(3) – ƒ( − 2) 3 − ( − 2) By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 3) such that ƒ'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
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