4. Suppose that fis continuous on [a, b] and f(a) < k < f(b). (a) Show that the proof of the IVT generates the largest c e [a, b] for which f(c) = k. (b) How could the set {x E [a, b] | f(x) > k} be used to find the smallest c e [a, b] for which f(c) = k? %3D

4. Suppose that fis continuous on [a, b] and f(a) < k < f(b). (a) Show that the proof of the IVT generates the largest c e [a, b] for which f(c) = k. (b) How could the set {x E [a, b] | f(x) > k} be used to find the smallest c e [a, b] for which f(c) = k? %3D

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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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4. Suppose that f is continuous on [a, b] and f(a) < k < f(b).
(a) Show that the proof of the IVT generates the largest c e [a,
b] for which f(c) = k.
(b) How could the set {x e [a, b] | f(x) > k} be used to find the
smallest c e [a, b] for which f(c) = k?

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