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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 44E

To determine

**To identify:** Each curves on the given graph and give proper explanation.

Expert Solution

In the given graph, *d* is position curve, *c* is velocity curve, *b* is acceleration curve and *a* is the jerk curve.

**Note:** Let *f* and *a* is *x*-coordinate of the point where *f* has horizontal tangent.

**Graph:**

The given graph is shown as in Figure 1,

**Observation:**

From Figure 1, the point where

Recall that the derivative of a function is zero where the function has a horizontal tangent.

The curve

Thus,

Observe the graph of *b* and *c* carefully.

The point where

Recall that the derivative of a function is zero where the function has a horizontal tangent.

The curve

Thus,

From (1) and (2),

There are two possibilities:

Observe the graph of *d* and *a* carefully.

The points where the graph of *a* has horizontal tangents, the functional value of *d* is not zero at that points.

This implies that

The only possibility is that *a* is the acceleration curve.

This implies

Thus *d* is position curve, *c* is velocity curve, *b* is acceleration curve and *a* is the jerk curve.