   Chapter 2.8, Problem 51E

Chapter
Section
Textbook Problem

The figure shows the graphs of three functions. One is the position function of a car, one is the velocity of the car, and one is its acceleration. Identify each curve, and explain your choices. To determine

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

Explanation

Graph:

The given graph is shown as in Figure 1,

Observation:

Observe the graph of b and a carefully.

The point where a(t)=0 is the same point where graph of b(t) has horizontal tangent.

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

Therefore, a(t) is the derivative of the graph b(t). That is, b(t)=a(t).

Observe the graph of a and c carefully

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