Concept explainers
(a)
Determine the maximum volume from the given table.
(a)
Answer to Problem 61E
The maximum volume from the given table is
Explanation of Solution
Given:
Consider an open box of maximum volume (in form of cuboid) with following dimensions.
Length is
Breath is
Height is x
Also,
Height, x | 1 | 2 | 3 | 4 | 5 | 6 |
Volume, V | 484 | 800 | 972 | 1024 | 980 | 864 |
Let estimate the maximum volume from the table.
From the table it is observe that height with
(b)
Plot the graph from the table obtained in part (a).
(b)
Answer to Problem 61E
Graph is shown below.
Explanation of Solution
Given:
Consider an open box of maximum volume (in form of cuboid) with following dimensions.
Length is
Breath is
Height is x
Let plot the graph for the points height and volume
Graphically, each value of height,
(c)
Find the function and determine the domain.
(c)
Answer to Problem 61E
The function is :
The domain is
Explanation of Solution
Given:
V is a function of x
V is a function of x.
Let the function of V in terms of x.
Volume of cuboid is length × breadth × height
Hence, V is as function of x.
Now find the domain of the function. Since height and volume cannot be negative or 0.
Therefore,
Then
Hence, the domain is
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
- 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