To determine To prove that a continuously differentiable function g ( x ) satisfying | g ' ( x ) | < 1 on a closed interval cannot have two fixed points on that interval. Explanation Given information : The function g ( x ) is a continuously differentiable function. Concept used : Check convergence on two different fixed points. Proof : Assume that there are two fixed points r 1 , r 2 for the continuously differentiable function g ( x ) = y in the closed interval [ a , b ] . If r 1 is the fixed point, it is clear that the fixed point iteration will converge to r 1

3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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Chapter 1.2, Problem 26E

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To prove that a continuously differentiable function g(x) satisfying |g'(x)|<1 on a closed interval cannot have two fixed points on that interval.

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Chapter 1.2, Problem 25E

Chapter 1.2, Problem 27E

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To prove that a continuously differentiable function g ( x ) satisfying | g ' ( x ) | &lt; 1 on a closed interval cannot have two fixed points on that interval.

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To prove that a continuously differentiable function g(x) satisfying |g'(x)|<1 on a closed interval cannot have two fixed points on that interval.

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Chapter 1 Solutions

To prove that a continuously differentiable function g ( x ) satisfying | g ' ( x ) | < 1 on a closed interval cannot have two fixed points on that interval.