An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see fi X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Volume, V 1[302(1)]2= 784 30 - 2(1) 30 2(2) 2[302(2)]²= 1352 302(3) 3[302(3)]²= 4 302(4) 4[30-2(4)]²= 5 302(5) 5[302(5)]²= 30-2(6) 6[302(6)]²=| Height, x V = 1 2 3 s-2x- 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. I 0 < x < 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see fi X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Volume, V 1[302(1)]2= 784 30 - 2(1) 30 2(2) 2[302(2)]²= 1352 302(3) 3[302(3)]²= 4 302(4) 4[30-2(4)]²= 5 302(5) 5[302(5)]²= 30-2(6) 6[302(6)]²=| Height, x V = 1 2 3 s-2x- 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. I 0 < x < 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
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...
Related questions
Question
100%
![An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
2x
X
V =
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
30 - 2(1)
30 - 2(2)
30 2(3)
30 - 2(4)
Height, x
1
2
3
4
5
6
s-2x-
30 - 2(5)
30 - 2(6)
X
I
Volume, V
1[30 – 2(1)]² = 784
2[30 – 2(2)]² = 1352
3[30 – 2(3)]² =
=
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
4[30 – 2(4)]² :
=
5[30 – 2(5)]²=
6[30 – 2(6)]² =
0 < x < 15
=
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =
(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba58da1-aa6c-4b34-ac65-53856b97f0bf%2F3b3a32c8-bdab-4ba8-9dc6-3adcb52fa60c%2F0wl1q8a_processed.png&w=3840&q=75)
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
2x
X
V =
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
30 - 2(1)
30 - 2(2)
30 2(3)
30 - 2(4)
Height, x
1
2
3
4
5
6
s-2x-
30 - 2(5)
30 - 2(6)
X
I
Volume, V
1[30 – 2(1)]² = 784
2[30 – 2(2)]² = 1352
3[30 – 2(3)]² =
=
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
4[30 – 2(4)]² :
=
5[30 – 2(5)]²=
6[30 – 2(6)]² =
0 < x < 15
=
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =
(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
Expert Solution
Step 1: given
An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides.
let the length of the sides of the square corners cut be x inches.
Step by step
Solved in 6 steps with 7 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning