Chapter 2.8, Problem 16E

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8th Edition

James Stewart

ISBN: 9781305270336

Textbook Problem

Make a careful sketch of the graph if .*f* and below it sketch the graph of *f'* in the same manner as in Exercises 4-11. Can you guess a formula for *f'*(*x*) from its graph?

*f*(*x*) = sin *x*

To determine

**To sketch:** The graph of

Explanation

The given function is

Recall the fact that, the derivative of a function at

From the graph, it is observed that the graph has a horizontal tangent at three points. Let the points be *A, B, C* and *D*. At these points, the derivative will be zero.

The AB section of the graph has negative slope which implies that the derivative will be negative in the section.

The BC section of the graph has positive slope which implies that the derivative will be positive in the section.

The CD section of the graph has negative slope which implies that the derivative will be negative in the section

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