3. Assume that f(x) is continuous on [a, b] and x1, x2,...,n are arbitrary numbers taken from [a, b]. Show that there exists c = (a, b) so that f(c) = = 1 [ƒ(x₁) + f(x₂)+...+ f(x)]. n Hint. Use Intermediate and Extreme Value Theorems.
3. Assume that f(x) is continuous on [a, b] and x1, x2,...,n are arbitrary numbers taken from [a, b]. Show that there exists c = (a, b) so that f(c) = = 1 [ƒ(x₁) + f(x₂)+...+ f(x)]. n Hint. Use Intermediate and Extreme Value Theorems.
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...
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![3. Assume that f(x) is continuous on [a, b] and x₁,x2,...,n are arbitrary numbers taken from [a, b].
Show that there exists c E (a, b) so that
f(c)
1
· [ƒ(x1) + ƒ(x2) + ... + f(xn)].
n
==
Hint. Use Intermediate and Extreme Value Theorems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca54911f-4c33-48b6-9518-41b412a01cf9%2Ff96537bb-0dba-4788-90e1-757daa0f98f9%2F89u7yx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Assume that f(x) is continuous on [a, b] and x₁,x2,...,n are arbitrary numbers taken from [a, b].
Show that there exists c E (a, b) so that
f(c)
1
· [ƒ(x1) + ƒ(x2) + ... + f(xn)].
n
==
Hint. Use Intermediate and Extreme Value Theorems.
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