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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

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

Chapter 2.8, Problem 52E, The figure shows the graphs of four functions. One is the position function of a car, one is the

To determine

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

Explanation

Note: Let f and f be the graph of a function and its derivative on the same screen. Then f(a)=0 where 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 a(t)=0 is the same point where graph of b(t) has horizontal slope.

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

The curve a(t) is the derivative of the graph b(t).

Thus, b(t)=a(t). (1)

Observe the graph of b and c carefully.

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

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

The curve b(t) is the derivative of the graph c(t).

Thus, c(t)=b(t)

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