1. Let f(x) = x', a = -1, b = 1. Verify that there is no number c for which f (b) – f(a) b - a | f'(c) = Explain why this does not contradict the mean value theorem.
1. Let f(x) = x', a = -1, b = 1. Verify that there is no number c for which f (b) – f(a) b - a | f'(c) = Explain why this does not contradict the mean value theorem.
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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![1. Let \( f(x) = x^{-1} \), \( a = -1 \), \( b = 1 \). Verify that there is no number \( c \) for which
\[
f'(c) = \frac{f(b) - f(a)}{b - a}.
\]
Explain why this does not contradict the mean value theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e8cc1e-1513-4d19-9b4e-e77f4807c795%2F5670d497-cf17-4c77-84e9-d663001c8503%2F3eq6raw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let \( f(x) = x^{-1} \), \( a = -1 \), \( b = 1 \). Verify that there is no number \( c \) for which
\[
f'(c) = \frac{f(b) - f(a)}{b - a}.
\]
Explain why this does not contradict the mean value theorem.
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