Chapter 2.8, Problem 4E

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8th Edition

James Stewart

ISBN: 9781305270343

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 derivative of *f* below the graph of *f.*

Explanation

From the given graph, it is observed that the graph of *f* contains the horizontal tangents at the three points. Let the three points be *A*, *B* and *C*.

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*, *B* and *C*.

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

From the points between *A* and *B*, the slope of the graph *f* is strictly positive which implies that the derivative graph

And, the slope of the graph *f* between the points *B* and *C* is strictly negative, which implies that the derivative graph

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P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-1PCh-2 P-2PCh-2 P-3PCh-2 P-4PCh-2 P-5PCh-2 P-6PCh-2 P-7PCh-2 P-8PCh-2 P-9PCh-2 P-10PCh-2 P-11PCh-2 P-12PCh-2 P-13PCh-2 P-14P

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