Consider the function f(x) = 6 – 2x on the interval [ - 2, 8]. Find the average or mean slope of the function on this interval, i.e. f(8) – f( – 2) 8 - (– 2) By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 8) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
Consider the function f(x) = 6 – 2x on the interval [- 2, 8]. Find the average or mean slope of the
function on this interval, i.e.
f(8) – f( – 2)
8 - (– 2)
By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 8) 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) = 6 – 2x on the interval [- 2, 8]. Find the average or mean slope of the function on this interval, i.e. f(8) – f( – 2) 8 - (– 2) By the Mean Value Theorem, we know there exists a c in the open interval ( – 2, 8) 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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