Explanation Given information: The statement “Every critical point of f is either a local maximum or local minimum of f ” Occurrence of local extrema: All local extrema occur at critical points, but not all critical points occur at local extrema. For any function f, a point p in the domain of f where f ‘ ( p ) = 0 or f ‘ ( p ) is undefined is called a critical point of the function. In addition, the point ( p , f ( p ) ) on the graph of f is also called a critical point. A critical value of f is the value, f ( p ) , at a critical point, p Geometrically, at the critical point where f ‘ ( p ) = 0 , the line tangent to the graph of f at p is horizontal

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4, Problem 8SYU

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

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Solution Summary: The author explains that the statement "Every critical point of f is either a local maximum or local minimum" is true or false.