Explanation Given information: The given statement is, “Each derivative is either positive everywhere, zero everywhere, or negative everywhere”. The given function, y = f ( x ) : Calculation: The term d y / d x represents the first order derivative i.e. slope of the graph. By the definition f ' ( x ) = d y / d x = Change in y Change in x As the graph is a straight line parallel to x -axis and here the change in y is zero. f ' ( x ) = d y / d x = 0 Numerical value = 0 Hence the first derivative is zero everywhere

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 2.4, Problem 5P

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The sign of the first and second derivatives for the function.

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Chapter 2.4, Problem 4P

Chapter 2.4, Problem 6P

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The sign of the first and second derivatives for the function.

Solution Summary: The author explains the sign of the first and second derivatives for the function. The graph is a straight line parallel to x -axis and the change in y is zero.

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Chapter 2 Solutions

To write:

The sign of the first and second derivatives for the function.