In the activities in chapter 1, you saw many examples of functions and their derivatives. Graphs are a great way to tell a story about the relationship between two quantities. Derivatives add important information about a situation. Here is one example: Temperature over Time temperature, (°F) 80 75 70 60 55 50 45 40 35 30 25 20 15 10 5 O 1 2 3 4 5 6 7 8 9 10 11 12 t, (hours) The units of the derivative f' (t) are deg. F per hour. The graph shows the outside temperature, in degrees Fahrenheit, as a function of time (in hours) between midnight and 12 pm. At midnight the temperature started at about 45 degrees, then the temperature dropped to 40 degrees by 3 am. From 3 am to 12 pm the temperature increased, reaching about 75 degrees at noon. In this situation, the derivative tells us how fast the temperature is changing at any particular time. For example, we have f' (8) 5 deg. F per hour. This tells us that at 8 am the temperature is increasing at a rate of about 5 degrees F per hour. Assignment: • Find an example of a function that you find interesting and show its graph (please do not use temperature as in the example). You can find graphs by o looking at newspapers or online sources, o making your own graph, o using examples from one of the activities in Chapter 1 or other course materials. • Write a couple of sentences to describe the story the graph is telling. • What are the units of the derivative? • Estimate the derivative at a point on the graph. • What does the derivative tell you about the situation in your example? • What questions do you have about derivatives? Make an illustration that tells the story of your example. At a minimum, include all the elements from the list. Feel free to add additional elements to make your story more compelling.
In the activities in chapter 1, you saw many examples of functions and their derivatives. Graphs are a great way to tell a story about the relationship between two quantities. Derivatives add important information about a situation. Here is one example: Temperature over Time temperature, (°F) 80 75 70 60 55 50 45 40 35 30 25 20 15 10 5 O 1 2 3 4 5 6 7 8 9 10 11 12 t, (hours) The units of the derivative f' (t) are deg. F per hour. The graph shows the outside temperature, in degrees Fahrenheit, as a function of time (in hours) between midnight and 12 pm. At midnight the temperature started at about 45 degrees, then the temperature dropped to 40 degrees by 3 am. From 3 am to 12 pm the temperature increased, reaching about 75 degrees at noon. In this situation, the derivative tells us how fast the temperature is changing at any particular time. For example, we have f' (8) 5 deg. F per hour. This tells us that at 8 am the temperature is increasing at a rate of about 5 degrees F per hour. Assignment: • Find an example of a function that you find interesting and show its graph (please do not use temperature as in the example). You can find graphs by o looking at newspapers or online sources, o making your own graph, o using examples from one of the activities in Chapter 1 or other course materials. • Write a couple of sentences to describe the story the graph is telling. • What are the units of the derivative? • Estimate the derivative at a point on the graph. • What does the derivative tell you about the situation in your example? • What questions do you have about derivatives? Make an illustration that tells the story of your example. At a minimum, include all the elements from the list. Feel free to add additional elements to make your story more compelling.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.5: Graphical Differentiation
Problem 19E: Human Growth The growth remaining in sitting height at consecutive skeletal age levels for boys is...
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Transcribed Image Text:Homework 8
In the activities in chapter 1, you saw many examples of functions and their derivatives. Graphs are a great way to tell a story
about the relationship between two quantities. Derivatives add important information about a situation. Here is one example:
Temperature over Time
temperature, (°F)
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
O
1
2 3
4
5
6 7 8
9
10 11 12
t, (hours)
The units of the derivative f' (t) are deg. F per
hour.
The graph shows the outside temperature, in degrees Fahrenheit, as a
function of time (in hours) between midnight and 12 pm. At midnight the
temperature started at about 45 degrees, then the temperature dropped to
40 degrees by 3 am. From 3 am to 12 pm the temperature increased,
reaching about 75 degrees at noon.
In this situation, the derivative tells us how fast the temperature is changing
at any particular time. For example, we have f' (8) ~ 5 deg. F per hour. This
tells us that at 8 am the temperature is increasing at a rate of about 5 degrees
F per hour.
Assignment:
• Find an example of a function that you find interesting and show its graph (please do not use temperature as in the example).
You can find graphs by
o looking at newspapers or online sources,
o making your own graph,
o using examples from one of the activities in Chapter 1 or other course materials.
• Write a couple of sentences to describe the story the graph is telling.
• What are the units of the derivative?
• Estimate the derivative at a point on the graph.
• What does the derivative tell you about the situation in your example?
• What questions do you have about derivatives?
Make an illustration that tells the story of your example. At a minimum, include all the elements from the list. Feel free to add
additional elements to make your story more compelling.
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