Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) 1 there,

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Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) ≤ 1 there, then f has a fixed point that is, there is a number c in [0, 1] such that f(c) = c.

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Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

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Question Posted: Jun 21, 2016 09:39 AM

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Prove that if f is continuous on [0, 1] and satisfies 0 s f(x) 1 there,

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Let gx x fx Then g0 0 f0 f0 0 and g1 1 f1 0 since 0 fx 1 on 0 1 I...View the full answer

Calculus

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