Concept explainers
(a)
To find: The quadratic polynomial that best fits the given data.
(a)
Answer to Problem 1P
The quadratic polynomial that best fits the given data is equal to
Explanation of Solution
Given information:
Car tires need to be inflated properly. Over inflation or under inflation can cause premature tread ware. The data and scatter plot given below show the tire life for different inflation values for a certain type of tire.
Pressure | Tire life |
Calculation:
Represent the tire life per thousand.
For the quadratic model of data follow the steps below:
First press the
Go to
Now enter the keystrokes
Figure(1)
Therefore, the quadratic polynomial that best fits the given data is equal to
(b)
To graph: The scatter plot of the given data and the quadratic polynomial obtained from part(a) in the same viewing window.
(b)
Explanation of Solution
Given information:
Car tires need to be inflated properly. Over inflation or under inflation can cause premature tread ware. The data and scatter plot given below show the tire life for different inflation values for a certain type of tire.
Pressure | Tire life |
Graph:
To graph the points on scatter plot, follow the steps using graphing calculator.
First press the
Go to
Now press the key
Now, press the
Figure (2)
(c)
To find: The pressure that gives the longest tire life with the help of results in part(b).
(c)
Answer to Problem 1P
The pressure that gives longest tire life is
Explanation of Solution
Given information:
Car tires need to be inflated properly. Over inflation or under inflation can cause premature tread ware. The data and scatter plot given below show the tire life for different inflation values for a certain type of tire.
Pressure | Tire life |
Calculation:
As observed from the graph of the function in part(b), the function achieves the maximum value at
So, the maximum long life of tires is at the tire pressure of maximum value.
Therefore, the pressure that gives longest tire life is
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning