Explanation Given information: The statement “If f ' ( p ) = 0 and f ' ' ( p ) > 0 then f has a local maximum at p .” The second derivative of a function can also be useful in testing if a critical point is a local maximum or local minimum . Suppose p is a critical point of f , with f ' ( p ) = 0 , so that the graph of f has a horizontal tangent line at p. If the graph is concave up at p, the f has a local minimum at p. Likewise, if the graph is concave down, f has a local maximum. The second-derivative test for local maximum and minima : Suppose p is a critical point of a continuous function f, and f ' ( p ) = 0

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Whether the statement is true or false.

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains how the second derivative of a function can be useful in testing if the critical point is local maximum or local minimum.