Question

The position (in thousands of feet) of a car driving along a straight road at time $t$ in minutes is given by the function $y = s(t)$ that is pictured below. 14 10 6 2 2 6 10 Which graph A-F is the best representative of the derivative function $s'(t)$? 10 Which of the following statements are true? Select all that apply. A. When $s'(t)$ is zero, the car is stopped. B. The function $s'$ represents the velocity of the car. C. If $s'(t)$ is zero, then $s(t)$ must be zero. D. When $s'(t)$ is positive, the car's position is increasing. E. The function $s'$ represents the acceleration of the car. F. When the car slows down, $s'(t)$ is negative. G. When $s'(t)$ is positive, the car's position is decreasing. H. None of the above statements are true. D E (Note: the vertical axes of these graphs may have been scaled to to fit these functions. Click on a graph to enlarge it.)

          The position (in thousands of feet) of a car driving along a straight road at time $t$ in minutes is given by the function $y = s(t)$ that is pictured below.
14
10
6
2
2
6
10
Which graph A-F is the best representative of the derivative function $s'(t)$?
10
Which of the following statements are true? Select all that apply.
A. When $s'(t)$ is zero, the car is stopped.
B. The function $s'$ represents the velocity of the car.
C. If $s'(t)$ is zero, then $s(t)$ must be zero.
D. When $s'(t)$ is positive, the car's position is increasing.
E. The function $s'$ represents the acceleration of the car.
F. When the car slows down, $s'(t)$ is negative.
G. When $s'(t)$ is positive, the car's position is decreasing.
H. None of the above statements are true.
D
E
(Note: the vertical axes of these graphs may have been scaled to to fit these functions. Click on a graph to enlarge it.)

Show more…

The position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y = s(t) that is pictured below.
14
10
6
2
2
6
10
Which graph A-F is the best representative of the derivative function s'(t)?
10
Which of the following statements are true? Select all that apply.
A. When s'(t) is zero, the car is stopped.
B. The function s' represents the velocity of the car.
C. If s'(t) is zero, then s(t) must be zero.
D. When s'(t) is positive, the car's position is increasing.
E. The function s' represents the acceleration of the car.
F. When the car slows down, s'(t) is negative.
G. When s'(t) is positive, the car's position is decreasing.
H. None of the above statements are true.
D
E
(Note: the vertical axes of these graphs may have been scaled to to fit these functions. Click on a graph to enlarge it.)

Added by James C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Christopher Stanley

01/26/2022

Step 1

When s'(t) is zero, the car is stopped - True, because when the derivative of the position function is zero, it means the car is not moving. B. The function s' represents the velocity of the car - True, because the derivative of the position function gives the Show more…

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I have posted the same question before and it has not been answered. Can someone please carefully address this calculus problem and help me figure out how to solve it? Thanks in advance. Which of the following statements are true? Select all that apply: A. When s'(t) is zero, the car is stopped. B. The function s' represents the velocity of the car. C. If s'(t) is zero, then s(t) must be zero. D. When s'(t) is positive, the car's position is increasing. E. The function s' represents the acceleration of the car. F. When the car slows down, s'(t) is negative. G. When s'(t) is positive, the car's position is decreasing. H. None of the above statements are true. Which graph A-F is the best representative of the derivative function st? Which of the following statements are true? Select all that apply: A. When s(t) is zero, the car is stopped. B. The function s represents the velocity of the car. C. If st is zero, then st must be zero. D. When a(t) is positive, the car's position is increasing. E. The function s represents the acceleration of the car. F. When the car slows down, s(t) is negative. G. When t is positive, the car's position is decreasing. H. None of the above statements are true.

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Transcript

00:01 All right, on this problem, we've been given an original function and looks something like this.

00:09 It's like it goes up and then takes a little bit of a stop, goes up, takes a little bit of a stop, and then so on.

00:16 Now, what we're wanting to do here is find the graph that represents the derivative of this function, the derivative of this function.

00:29 First time it stops is at about two, and it stops until what looks like to be about three and a half.

00:35 So from two, the three and a half here, it stops.

00:38 Now, because from 2 to 3 .5, it doesn't do anything at all.

00:43 It means its derivative is 0.

00:45 So from 2 to about 3 .5 for the derivative, the derivative is zero there.

00:52 Okay, because it just stalled out there, the derivative is zero there.

00:57 Now, it's a similar for these next points here.

00:59 Somewhere between right there and somewhere there on the end.

01:04 So it means similarly between about 4 .5 to 7.

01:14 And from 9 to 10.

01:15 About 4 .5 to 7 and 9 to 10.

01:17 The derivative should be zero.

01:18 So it's going to need to be on this x -axis quite a bit here, okay, quite a bit, which most of ours are.

01:28 Okay, but you can automatically get rid of d because it doesn't do that.

01:34 Everywhere else, it's positive.

01:35 The derivative is, this slope is always positive.

01:38 So since that slope is always positive, it means the derivative is always positive.

01:42 Okay, the derivative is always positive.

01:44 So the derivative should always be up here somewhere, okay, because it's always positive.

01:47 Always got to be positive, which means you can automatically throw out b, f, and e.

01:57 B, f, and e.

01:58 It only leaves us with a and c.

02:01 You'll notice on a, it doesn't stay zero for very long there on a.

02:06 It doesn't really hover at zero very much...

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