Let I:= [a,b] and let f: I - IR be a continuousfunctioN ON I such that for each x in I there existsX IN<Y IN I such that | F(Y)| ≤ = | f(x). Prove there existsa point C IN I such that f(c) = 0.

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Answered: Let I:= [a,b] and let f: I - IR be a…

Let I:= [a,b] and let f: I - IR be a continuous functioN ON I such that for each X IN I there exists Y a point c iN I such that | F(y) | ≤ = |f(x)). Prove there exists L IN I such that f(c) = 0.

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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Question

Let I:= [a,b] and let f: I - IR be a continuous
functioN ON I such that for each x in I there exists
X IN
<
Y IN I such that | F(Y)| ≤ = | f(x). Prove there exists
a point C IN I such that f(c) = 0.

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I can't follow any of the writing. Some of it is dim, and some doesn't make sense:

In the problem, we assume f(c) = 0

But then we say, "Let there exist a c in I such that 0<|f(c)| <= |f(x)|

Why??

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