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 5.2, Problem 4E

To determine

To state : Whether or not the function satisfies the hypothesis of the Mean Value Theorem on the given interval.

Expert Solution

Answer to Problem 4E

The function f(x)=|x−1| does not satisfy the hypothesis of Mean Value Theorem.

Explanation of Solution

Given information :

The given function is f(x)=|x−1| on [0, 4]

Calculation :

The function f(x) satisfies the hypothesis of the Mean Value Theorem if f(x) is continuous at every point of the closed interval [a, b] and differentiable at every point of its interior (a, b) .

Consider the given function:

f(x)=|x−1| on [0, 4]

The absolute value function |x| has a corner at x=0 . The given function is f(x)=|x−1| , which means the graph of f(x) is shifted 1 unit right, so f(x) has a corner at x=1 .

Therefore, the function f(x) is no longer differentiable on (0, 4) .

Since, to satisfy the hypothesis of Mean Value Theorem the function f(x) should be differentiable at every point of its interior (0, 4) . But, here the function f(x) is not differentiable at point 1 which is interior of (0, 4) .

Hence,

The function f(x)=|x−1| does not satisfy the hypothesis of Mean Value Theorem.

To determine

To find : Value of c in the interval (a, b) that satisfies the equation f'(c)=f(b)−f(a)b−a .

Expert Solution

Answer to Problem 4E

The value of c does not exist.

Explanation of Solution

Given information :

The given function is f(x)=|x−1| on [0, 4]

Calculation :

From (a) the function f(x) does not satisfies the hypothesis of Mean Value Theorem. Therefore, there the value of c does not exist.

Hence,

The value of c does not exist.

Chapter 5.2, Problem 3E

Chapter 5.2, Problem 5E

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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