Use the equation to establish the following test. Let have continuous first and second derivatives and

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Use the equationimage


to establish the following test. Let ƒ have continuous first and second derivatives and suppose that ƒ′(a) = 0. Then


a. ƒ has a local maximum at a if ƒ″ ≤ 0 throughout an interval whose interior contains a;


b. ƒ has a local minimum at a if ƒ″ ≥ 0 throughout an interval whose interior contains a.

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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