PROBLEMS 11.3 1. Suppose that the position function of an object moving along a straight line is s =f(t) = 21² + 3t, where t is in seconds and s is in meters. Find the average velocity As/At over the interval [1, 1+ At], where At is given in the following At 1 0.5 0.2 0.1 0.01 0.001 %3D As/At From your results, estimate the velocity when t = 1. Verify your estimate by using differentiation. table:
PROBLEMS 11.3 1. Suppose that the position function of an object moving along a straight line is s =f(t) = 21² + 3t, where t is in seconds and s is in meters. Find the average velocity As/At over the interval [1, 1+ At], where At is given in the following At 1 0.5 0.2 0.1 0.01 0.001 %3D As/At From your results, estimate the velocity when t = 1. Verify your estimate by using differentiation. table:
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
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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![rates of of with respect
(x))
EXAMPLE 9
Relative and Percentage Rates of Change
APPLY IT
Determine the relative and percentage rates of change of
5. The volume V enclosed by a capsule-
shaped container with a cylindrical
height of 4 feet and radius r is given by
y = f(x) = 3x² - 5x + 25
when x = 5.
= (d)A
3
4.
%3D
Solution: Here
Determine the relative and percentage
to the radius when the radius is 2 feet.
f'(x) = 6x - 5
Since f'(5) = 6(5) – 5 = 25 andf(5) = 3(5) – 5(5) + 25 = 75, the relative rate of
change of y when x = 5 is
%3D
%3D
f'(5)
25
~0.333
75
Multiplying 0.333 by 100% gives the percentage rate of change: (0.333)(100) = 33.3%.
f(5)
Now Work Problem 354
PROBLEMS 11.3
1. Suppose that the position function of an object moving
along a straight line is s =f(t) = 2t² + 3t, where t is in
seconds and s is in meters. Find the average velocity As/At
over the interval [1, 1 + At], where At is given in the following
0.5
1.
0.2 0.1
0.01
%3D
From your results, estimate the velocity whent= 1. Verify your
estimate by using differentiation.
table:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2d6f28-e3d7-414c-b1d4-a752131175c2%2F50e1477a-af54-4e65-b4fd-6b2de8ecbd66%2F1ubxttn.jpeg&w=3840&q=75)
Transcribed Image Text:rates of of with respect
(x))
EXAMPLE 9
Relative and Percentage Rates of Change
APPLY IT
Determine the relative and percentage rates of change of
5. The volume V enclosed by a capsule-
shaped container with a cylindrical
height of 4 feet and radius r is given by
y = f(x) = 3x² - 5x + 25
when x = 5.
= (d)A
3
4.
%3D
Solution: Here
Determine the relative and percentage
to the radius when the radius is 2 feet.
f'(x) = 6x - 5
Since f'(5) = 6(5) – 5 = 25 andf(5) = 3(5) – 5(5) + 25 = 75, the relative rate of
change of y when x = 5 is
%3D
%3D
f'(5)
25
~0.333
75
Multiplying 0.333 by 100% gives the percentage rate of change: (0.333)(100) = 33.3%.
f(5)
Now Work Problem 354
PROBLEMS 11.3
1. Suppose that the position function of an object moving
along a straight line is s =f(t) = 2t² + 3t, where t is in
seconds and s is in meters. Find the average velocity As/At
over the interval [1, 1 + At], where At is given in the following
0.5
1.
0.2 0.1
0.01
%3D
From your results, estimate the velocity whent= 1. Verify your
estimate by using differentiation.
table:
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