1. Prove that f is a continuous function at [0, 1] and satisfies 0 < f(x) < 1, then there is c such that f(c) = c. Hint: Use Intermediate Value Theorem for g(x) = x - f(x)
1. Prove that f is a continuous function at [0, 1] and satisfies 0 < f(x) < 1, then there is c such that f(c) = c. Hint: Use Intermediate Value Theorem for g(x) = x - f(x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Prove that f is a continuous function at [0, 1] and satisfies 0 < f(x) < 1,
then there is c such that f(c) = C.
Hint: Use Intermediate Value Theorem for g(x) = x - f(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2482e0eb-dd9b-4353-b754-c42e8558d084%2F193f1a6e-56f6-4482-a54a-616656288228%2F2vb2t2a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove that f is a continuous function at [0, 1] and satisfies 0 < f(x) < 1,
then there is c such that f(c) = C.
Hint: Use Intermediate Value Theorem for g(x) = x - f(x)
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