Let f R R be defined by f(x) 2x4 x4 sin(1 x) for x 0 and f(0) 0 Show that f has an absolute minimum at x 0, but that its derivative has both positive and negative values in every neighborhood of 0 ...

fx x 4 2 sin1x 0 for all x 0 so f h ...

Let f : R R be defined by f(x) := 2x4 + x4 sin(1/x) for x

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Let f : R → R be defined by f(x) := 2x4 + x4 sin(1/x) for x ≠ 0 and f(0) := 0. Show that f has an absolute minimum at x ¼ 0, but that its derivative has both positive and negative values in every neighborhood of 0.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 11:03 AM

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Let f : R R be defined by f(x) := 2x4 + x4 sin(1/x) for x

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Introduction to Real Analysis

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