Explanation Given information: The statement “If f ' ( p ) = 0 and f ' ' ( p ) > 0 then p is a global minimum of f ” From the given statement, we can conclude that given function has local minimum at p using second derivative test, but there is not enough information to tell that function has global minimum of f 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

6th Edition

ISBN: 9781119399322

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 30SYU

To determine

To indicate:

Whether the statement is true or false.

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Chapter 4, Problem 29SYU

Chapter 4, Problem 31SYU

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that the statement "If f'(p)=0 is false," but there is not enough information to tell that function has global minimum at p.