Explanation The graph of the given function plotted below indicates that there exists a derivative at x = 3 . Also, there exists a horizontal tangent line at this point. Given: f ( x ) = ( x − 3 ) 5 / 3 , a = 3 Calculation: The graph of f ( x ) =

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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 3.2, Problem 78E

To determine

The plotting of f at the point (a, f(a)) if f is differentiable at x = a. If not, state if the tangent line appears vertical or does not exist

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Chapter 3.2, Problem 77E

Chapter 3.2, Problem 79E

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Chapter 3 Solutions

Calculus - Standalone book

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

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The plotting of f at the point ( a , f ( a ) ) if f is differentiable at x = a . If not, state if the tangent line appears vertical or does not exist

Solution Summary: The author explains that the graph of f indicates that there exists a derivative at

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The plotting of f at the point (a, f(a)) if f is differentiable at x = a. If not, state if the tangent line appears vertical or does not exist

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Chapter 3 Solutions