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If functions f and g are continuous on the interval [-1, 1] and differ- entiable on (-1, 1), and they satisfy f(-1) = f(1) and g(-1) = g(1), prove that there exists some { E (-1,1) such that f'(E) = g'(£)f(E).

If functions f and g are continuous on the interval [-1, 1] and differ- entiable on (-1, 1), and they satisfy f(-1) = f(1) and g(-1) = g(1), prove that there exists some { E (-1,1) such that f'(E) = g'(£)f(E).

Calculus: Early Transcendentals
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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If functions f and g are continuous on the interval [-1, 1] and differ- entiable on (-1, 1), and they satisfy f(-1) = f(1) and g(-1) = g(1), prove that there exists some { E (-1,1) such that f'(E) = g'(£)f(£).
Transcribed Image Text:If functions f and g are continuous on the interval [-1, 1] and differ- entiable on (-1, 1), and they satisfy f(-1) = f(1) and g(-1) = g(1), prove that there exists some { E (-1,1) such that f'(E) = g'(£)f(£).
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