An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= =
An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= =
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 66E: Fabricating sheet metal The open tray shown in the illustration is to be manufactured from a...
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![An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).
XT
-x7-8
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
24 - 2(1)
24 - 2(2)
24 2(3)
V
Height, X
1
2
3
4
5
s-2x
6
Volume, V
1[242(1)]2 484
2[24-2(2)]² = 800
3[24 - 2(3)]²= |
4[24 - 2(4)]²=
242(4)
242(5) 5[24 - 2(5)]² =
242(6)
6[242(6)]²=
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
0 < x < 12
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bd49b2c-271c-4419-b7df-972693879afc%2F0c2e9856-5b88-46da-84cb-aaa932eed200%2F3332eir_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 = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).
XT
-x7-8
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
24 - 2(1)
24 - 2(2)
24 2(3)
V
Height, X
1
2
3
4
5
s-2x
6
Volume, V
1[242(1)]2 484
2[24-2(2)]² = 800
3[24 - 2(3)]²= |
4[24 - 2(4)]²=
242(4)
242(5) 5[24 - 2(5)]² =
242(6)
6[242(6)]²=
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
0 < x < 12
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =
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Transcribed Image Text:Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
V
1000
800
600
400
200
V
1000
800
600
400
200
2
4
6 8
2 4 6 8
10
10
12
12
X
X
120
100
80
60
40
20
1
500
2
N
400
300
n
200
100
3
4
4
6
8
00
5
10
01
12
X
X
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