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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

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

Chapter 2.8, Problem 9E, Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use , example  1

FIGURE 1

Chapter 2.8, Problem 9E, Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use , example  2

FIGURE 2

Chapter 2.8, Problem 9E, Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use , example  3

Chapter 2.8, Problem 9E, Trace or copy the graph of the given function .f. (Assume that the axes have equal scales.) Then use , example  4

To determine

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

Explanation

From the graph, it is observed that the graph has a corner point at three points.

Let the three points be A, B and C. The derivative graph f is discontinuous at these points. That is, the derivative does not exist at these three points.

The graph from point A to B has negative slope which implies that the derivative graph must have negative value in this section. Since the function is linear in this part,

the derivative graph will be horizontal line.

The graph from point B to C has positive slope which implies that the derivative graph must have positive value in this section. Since the function is linear in this part,

the derivative graph will be horizontal line.

The graph from point C to D has negative slope which implies that the derivative graph must have a negative functional value

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