Let f: Rn R. Suppose that for each unit vector u Rn, the directional derivative

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Let f: Rn → R. Suppose that for each unit vector u ∈ Rn, the directional derivative Duf(a + tu) exists for t ∈ [0, 1 ] (see Definition 11.19). Prove that
f(a + u) - f(a) = Duf(a + tu)
for some t ∈ (0, 1).

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:21 AM

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Let f: Rn R. Suppose that for each unit vector u Rn, the directional derivative

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Let Ft fa tu and observe by definition that Thus F ...View the full answer

An Introduction to Analysis

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