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

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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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.