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

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 5.2, Problem 50E

To determine

To Prove: The fact that there is at least one point between a and b where the tangent to the graph of the f and g are parallel or the same line illustrate with the sketch.

Expert Solution & Answer

Explanation of Solution

Given:

Assume that the f and g are differentiable on the [a,b] and that f(a)=f(b) and f(b)=gb .

Calculation:

Consider that the mean value theorem show that the for continuous differentiable curve that connect the two points A and B there is the tangent line to the curve somewhere that is parallel to the connecting the two points that is chord AB. As bot the f and g passes through the points A and B then the tangent lines at the some point parallel to the chord AB and are parallel to each other.

Then, the graph obtained is shown in Figure 1

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.2, Problem 50E

Figure 1

Chapter 5.2, Problem 49E

Chapter 5.2, Problem 51E

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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Prob. 37E Ch. 5.4 - Prob. 38E Ch. 5.4 - Prob. 39E Ch. 5.4 - Prob. 40E Ch. 5.4 - Prob. 41E Ch. 5.4 - Prob. 42E Ch. 5.4 - Prob. 43E Ch. 5.4 - Prob. 44E Ch. 5.4 - Prob. 45E Ch. 5.4 - Prob. 46E Ch. 5.4 - Prob. 47E Ch. 5.4 - Prob. 48E Ch. 5.4 - Prob. 49E Ch. 5.4 - Prob. 50E Ch. 5.4 - Prob. 51E Ch. 5.4 - Prob. 52E Ch. 5.4 - Prob. 53E Ch. 5.4 - Prob. 54E Ch. 5.4 - Prob. 55E Ch. 5.4 - Prob. 56E Ch. 5.4 - Prob. 57E Ch. 5.4 - Prob. 58E Ch. 5.4 - Prob. 59E Ch. 5.4 - Prob. 60E Ch. 5.4 - Prob. 61E Ch. 5.4 - Prob. 62E Ch. 5.4 - Prob. 63E Ch. 5.4 - Prob. 64E Ch. 5.4 - Prob. 65E Ch. 5.5 - Prob. 1QR Ch. 5.5 - Prob. 2QR Ch. 5.5 - Prob. 3QR Ch. 5.5 - Prob. 4QR Ch. 5.5 - Prob. 5QR Ch. 5.5 - Prob. 6QR Ch. 5.5 - Prob. 7QR Ch. 5.5 - Prob. 8QR Ch. 5.5 - Prob. 9QR Ch. 5.5 - Prob. 10QR Ch. 5.5 - Prob. 1E Ch. 5.5 - Prob. 2E Ch. 5.5 - Prob. 3E Ch. 5.5 - Prob. 4E Ch. 5.5 - Prob. 5E Ch. 5.5 - Prob. 6E Ch. 5.5 - Prob. 7E Ch. 5.5 - Prob. 8E Ch. 5.5 - Prob. 9E Ch. 5.5 - Prob. 10E Ch. 5.5 - Prob. 11E Ch. 5.5 - Prob. 12E Ch. 5.5 - 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