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 2.7, Problem 4E
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 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 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 negative functional value.

From the points between A and B, the slope of the graph f is strictly positive which implies that the derivative graph f must have a positive functional value.

And, the slope of the graph f between the points B and C is strictly negative, which implies that the derivative graph f must have a negative functional value.

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

Use the above information and obtain the graph of f(x) as shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.7, Problem 4E

From Figure1, it is observed that the function f(x) passes through the point (0,0).

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