a. Explanation Given information: The function is f ( x ) = { sin 1 x , x > 0 0 , x = 0 } . Graph: to graph the function, plot some points x f ( x ) 0 0 1 sin 1 2 sin 1 2 Now, plot these points and join them and make a smooth curve, The graph can be observed as: Interpretation: from the above graph it can be observed that f ( 0 ) = 0 is not a local extreme value because in any open interval containing x = 0 , there are infinitely many points where f ' ( x ) = 1 and where f ' ( x ) = − 1 . b. To determine To find: the function that fails to have an extreme value at a domain endpoint. Answer The function is f ( x ) = { ( 1 − x ) cos 1 1 − x , 0 ≤ x < 1 0 , x = 1 } that fails to have an extreme value at a domain endpoint. Explanation Given information: The function is f ( x ) = { sin 1 x , x > 0 0 , x = 0 } . Calculation: the one possible function can be as on the interval [ 0 , 1 ] , f ( x ) = { ( 1 − x ) cos 1 1 − x , 0 ≤ x < 1 0 , x = 1 } The function has no local extreme value at x = 1 but it is continuous on [ 0 , 1 ] .

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

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

See similar textbooks

Question

Chapter 5.1, Problem 55E

To determine

To graph: that function.

Expert Solution

Explanation of Solution

Given information:

The function is f(x)={sin1x, x>00, x=0} .

Graph: to graph the function, plot some points

x	f(x)
0	0
1	sin1
2	sin12

Now, plot these points and join them and make a smooth curve,

The graph can be observed as:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.1, Problem 55E

Interpretation: from the above graph it can be observed that f(0)=0 is not a local extreme value because in any open interval containing x=0 , there are infinitely many points where f'(x)=1 and where f'(x)=−1 .

To determine

To find: the function that fails to have an extreme value at a domain endpoint.

Expert Solution

Answer to Problem 55E

The function is f(x)={(1−x)cos11−x, 0≤x<10, x=1} that fails to have an extreme value at a domain endpoint.

Explanation of Solution

Given information:

The function is f(x)={sin1x, x>00, x=0} .

Calculation: the one possible function can be as on the interval [0,1] ,

f(x)={(1−x)cos11−x, 0≤x<10, x=1}

The function has no local extreme value at x=1 but it is continuous on [0,1] .

Chapter 5.1, Problem 54E

Chapter 5.2, Problem 1QR

Chapter 5 Solutions

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

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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