BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2, Problem 36RE
To determine

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

Expert Solution

Explanation of 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 f will be zero at the points 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 f must have a functional value in negative.

From the point A to point B, the slope of the graph f is strictly positive which implies that the derivative graph f must have a functional value in positive.

From the point B to point C, the slope of the graph f is strictly negative which implies that the derivative graph f must have a functional value in negative.

From the point C to point D, the slope of the graph f is strictly positive which implies that the derivative graph f must have a functional value in positive.

From the graph, it is observed that the graph has a corner point at one point. Let the point be D. The derivative graph f is discontinuous at this point. That is, the derivative does not exist at the point 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.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2, Problem 36RE

Thus, f is the required graph.

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