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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 36RE

To determine

**To sketch:** The graph of derivative of *f* below the graph of *f.*

Expert Solution

From the given graph, it is observed that the graph of *f* contains horizontal tangents at three points. Let these 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 point *A* to point *B*, the slope of the graph *f* is strictly positive which implies that the derivative graph

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

From the point *C* to point *D*, the slope of the graph *f* is strictly positive which implies that the derivative graph

From the graph, it is observed that the graph has a corner point at one point. Let the point be *D*. The derivative graph *D*.

From the point *D* to right, the slope of the graph *f* is strictly negative, which implies that the derivative graph must have a functional value in negative. Since the function is linear in this part, the derivative graph will be horizontal line.

**Graph:**

Trace the graph of *f* and use the above information to draw the graph of its derivative directly beneath as shown below in Figure 1.

Thus,