The question is attached below. These are practice test question for an undergrad entrance exam. Please provide an intuition using a graph. There is no need to prove it only an intuitive reasoning (with figure) will be enough. I think the answer should be D. Thank you. 12. Let f : [0, 1] → R be differentiable and suppose that |f'(x)| < 1 for every r E [0, 1].Then, thereA. is at least one c e [0, 1] such that f(c) = c.B. are two numbers c and c2 such that f(c) = c; for i = 1, 2.C. is exactly one c € [0,1] such that f(c) = c.D. is at most one c e [0, 1] such that f(c) = c.

It is given that f'x<1 for every x∈0, 1 where the function fx is a differentiable function such…

Answered: 12. Let f : [0, 1] → R be…

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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The question is attached below. These are practice test question for an undergrad entrance exam. Please provide an intuition using a graph. There is no need to prove it only an intuitive reasoning (with figure) will be enough.

I think the answer should be D. 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 c and c2 such that f(c) = c; for i = 1, 2.
C. is exactly one c € [0,1] such that f(c) = c.
D. is at most one c e [0, 1] such that f(c) = c.

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