Answer the true statement for function is f ( − a ) a local maximum . Explanation Given information: If an even function f with domain all real numbers has a local maximum at x = a , then f ( − a ) , Is a local minimum Is a local maximum Is both a local minimum and a local maximum Could be either a local minimum or a local maximum Is neither a local minimum nor a local maximum. Calculation: since, the function is even and at the point x = a the local maximum is occur, It means that f ( a ) is a local maximum. Because the function is an even function, so substitute the value in function x = − a , f ( − a ) must be the local maximum.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.1, Problem 50E

To determine

To find: the true statement for the function.

Expert Solution & Answer

Answer to Problem 50E

the true statement for function is f(−a) a local maximum.

Explanation of Solution

Given information:

If an even function f with domain all real numbers has a local maximum at x=a , then f(−a) ,

Is a local minimum
Is a local maximum
Is both a local minimum and a local maximum
Could be either a local minimum or a local maximum
Is neither a local minimum nor a local maximum.

Calculation: since, the function is even and at the point x=a the local maximum is occur,

It means that f(a) is a local maximum.

Because the function is an even function, so substitute the value in function x=−a ,

f(−a) must be the local maximum.

Chapter 5.1, Problem 49E

Chapter 5.1, Problem 51E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

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