function notation for this.) b) What is the robot's average velocity (averare rate of change) between 2 seconds and 4 seconds? Be explicit in what you are calculating; use correct notation, and make sure to include units.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a) What is the robot's position two seconds after starting (t=2)? What is its position at t=4? (Use
function notation for this.)
b) What is the robot's average velocity (averare rate of change) between 2 seconds and 4
seconds? Be explicit in what you are calculating; use correct notation, and make sure to include
units.
c) Sketch the secant line with slope corresponding to the average velocity of the robot between
2 seconds and 4 seconds. Make sure you identify this line on the graph (you may label it "part
c").
d) Sketch the line with slope corresponding to the robot's (instant) velocity at 7 seconds. Again,
identify this line on the graph (use a different color if you can; label it).
e) Which of the following is a reasonable estimate for the robot's velocity at t=7?
I. s'(7) ~ 0 m/sec
II. s'(7) ~ 8 m/sec
III. s'(7) ~ -3 m/sec
IV. s' (7) is not defined
f) Explain your answer to part e), making a connection to the line that you sketched in part d).
Transcribed Image Text:a) What is the robot's position two seconds after starting (t=2)? What is its position at t=4? (Use function notation for this.) b) What is the robot's average velocity (averare rate of change) between 2 seconds and 4 seconds? Be explicit in what you are calculating; use correct notation, and make sure to include units. c) Sketch the secant line with slope corresponding to the average velocity of the robot between 2 seconds and 4 seconds. Make sure you identify this line on the graph (you may label it "part c"). d) Sketch the line with slope corresponding to the robot's (instant) velocity at 7 seconds. Again, identify this line on the graph (use a different color if you can; label it). e) Which of the following is a reasonable estimate for the robot's velocity at t=7? I. s'(7) ~ 0 m/sec II. s'(7) ~ 8 m/sec III. s'(7) ~ -3 m/sec IV. s' (7) is not defined f) Explain your answer to part e), making a connection to the line that you sketched in part d).
1.
A robot travels along a linear track corresponding to the distance-time graph shown
below (distance is measured in meters, time is measured in seconds).
Call this function s(t).
NOTE: You will be using this graph to sketch a couple of lines, so either print this page, of copy
this graph as closely as you can.
сopy
2.
4.
9.
10
Transcribed Image Text:1. A robot travels along a linear track corresponding to the distance-time graph shown below (distance is measured in meters, time is measured in seconds). Call this function s(t). NOTE: You will be using this graph to sketch a couple of lines, so either print this page, of copy this graph as closely as you can. сopy 2. 4. 9. 10
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