Let f : [0, 1] –→ R be differentiable and suppose that Then, there |f'(x)| < 1 for every x € [0, 1]. A. is at least one c e [0, 1] such that f(c) = c. B. are two numbers c1 and c2 such that f(ci) = c¡ for i = 1, 2. C. is exactly one c € [0, 1] such that f(c) = c. %3D D. is at most one c E [0, 1] such that f(c) = c. %3D
Let f : [0, 1] –→ R be differentiable and suppose that Then, there |f'(x)| < 1 for every x € [0, 1]. A. is at least one c e [0, 1] such that f(c) = c. B. are two numbers c1 and c2 such that f(ci) = c¡ for i = 1, 2. C. is exactly one c € [0, 1] such that f(c) = c. %3D D. is at most one c E [0, 1] such that f(c) = c. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
The question is attached in the image. Please provide an intuition for the correct answer (a figure would be helpful). Please provide a proof as well, if its possible. Thank you.
![12. Let f : [0, 1] → R be differentiable and suppose that |f'(x)| < 1 for every r E [0, 1].
Then, there
A. is at least one c E [0, 1] such that f(c) = c.
B. are two numbers c1 and c2 such that f(ci) =
= C; for i = 1, 2.
C. is exactly one c e [0, 1] such that f(c) = c.
D. is at most one c e [0, 1] such that f(c) = c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f4412a-18c0-4f64-8bcf-4dffb42656da%2F74332d9a-240e-4753-8f56-067c74d092e8%2Fdtnggfq_processed.png&w=3840&q=75)
Transcribed Image Text:12. Let f : [0, 1] → R be differentiable and suppose that |f'(x)| < 1 for every r E [0, 1].
Then, there
A. is at least one c E [0, 1] such that f(c) = c.
B. are two numbers c1 and c2 such that f(ci) =
= C; for i = 1, 2.
C. is exactly one c e [0, 1] such that f(c) = c.
D. is at most one c e [0, 1] such that f(c) = c.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
