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.
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.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 55E: Let T be a linear transformation from P2 into P2 such that T(1)=x,T(x)=1+xandT(x2)=1+x+x2. Find...
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe57a7d70-87de-4a1f-8104-5b2578062c6c%2Fbfba5cff-f286-45fc-a25a-b572a40520c9%2Fg40c9em_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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??
Solution
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