Explanation Given information: The statement “If f ' ( p ) = 0 then p is a critical point of f ” 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. At a critical point where f ’ ( p ) is undefined, there is no horizontal tangent to the graph-there is either a vertical tangent or no tangent at all

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Differential Equations

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Chapter 4, Problem 2SYU

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Whether the statement is true or false.

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Chapter 4 Solutions

APPLIED CALCULUS-WILEYPLUS

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that if f'(p)=0 is undefined, p is a critical point of the function.