Chapter 2.8, Problem 7E

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8th Edition

James Stewart

ISBN: 9781305270336

Textbook Problem

Trace or copy the graph of the given function .*f*. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of *f'* below it.

**Example 1**

**FIGURE 1**

**FIGURE 2**

To determine

**To sketch:** The graph of *f.*

Explanation

From the given graph, it is observed that the graph of *f* contains the horizontal tangent at one point. Let the point be *A*.

Note that, the value of the derivative will be zero at the point where the function has the horizontal tangent.

Thus, the graph of *A*.

From the given graph, *f* has a vertical tangent line at the left end point. This implies that, the derivative function *f* is not differentiable at that point.

From the point *A* to left, the slope of the graph *f* is positive which implies that the derivative graph

From the point *A* to right, the slope of the graph *f* is negative which implies that the derivative graph

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