Let f be a continuous function on [a,b]⊂R and f(x)∈[a,b] for all x∈[a,b]. Prove that there exists a point c in [a,b] at which f(c) =c. We call point c a fixed point of f. Hint: Apply the intermediate-value theorem to the function g(x) =f(x)−x

Let f be a continuous function on [a,b]⊂R and f(x)∈[a,b] for all x∈[a,b]. Prove that there exists a point c in [a,b] at which f(c) =c. We call point c a fixed point of f. Hint: Apply the intermediate-value theorem to the function g(x) =f(x)−x

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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