1. Let f : R n ---t R. Suppose that for each unit vector u ERn, the...

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

(a) = Duf(a+ tu)

for some t E (0,1).

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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Question Posted: Jul 20, 2024 05:02 AM

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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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1. Let f : R n ---t R. Suppose that for each unit vector u ERn, the...

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An Introduction To Analysis

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