   Chapter 2.8, Problem 52E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### 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. 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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