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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 14E

To determine

**To sketch:** The graph of

Expert Solution

The formula for

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.

**Graph:**

Use the online graphing calculator to draw the graph of

**Observation:**

From the Figure 1, it is observed that the graph of the derivative function seems to be the cosine function.

Thus, the formula of the derivative function is,