An open box of maximum volume is to be made from a square piece of material, s 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). S-2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 12 - 2(1) 1[12 - 2(1)]2 - 100 2. 12- 2(2) 2[12 - 2(2)]2 - 128 3. 12 - 2(3) 3[12 - 2(3)]? - | 4 12-2(4) 4[12 - 2(4)]? - 5 12-2(5) 5[12- 2(5)]? - | 6. 12- 2(6) 6[12 - 2(6)]? =
An open box of maximum volume is to be made from a square piece of material, s 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). S-2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 12 - 2(1) 1[12 - 2(1)]2 - 100 2. 12- 2(2) 2[12 - 2(2)]2 - 128 3. 12 - 2(3) 3[12 - 2(3)]? - | 4 12-2(4) 4[12 - 2(4)]? - 5 12-2(5) 5[12- 2(5)]? - | 6. 12- 2(6) 6[12 - 2(6)]? =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 39E
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![An open box of maximum volume is to be made from a square piece of material, s 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).
S- 2x
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Height, x
Length and
Width
Volume, V
12 - 2(1)
1[12 - 2(1)]² = 100
12-2(2)
2[12 - 2(2)]² - 128
3.
12 - 2(3) 3[12- 2(3)]? - |
4
12 - 2(4) 4[12 – 2(4)]² =
12 - 2(5) 5[12 – 2(5)]? |
6.
12 - 2(6) 6[12 – 2(6)]² =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa73689f3-cef9-455b-931c-3b4bd0aefe42%2Fc82933b0-3e37-4a6d-8c52-0b93e7ebb707%2Fcftkg4e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).
S- 2x
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Height, x
Length and
Width
Volume, V
12 - 2(1)
1[12 - 2(1)]² = 100
12-2(2)
2[12 - 2(2)]² - 128
3.
12 - 2(3) 3[12- 2(3)]? - |
4
12 - 2(4) 4[12 – 2(4)]² =
12 - 2(5) 5[12 – 2(5)]? |
6.
12 - 2(6) 6[12 – 2(6)]² =
Transcribed Image Text:Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
V =
0 <x < 6
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =
(d) Use a graphíng utility to graph the function in part (b) and verify the maximum volume from the graph.
V
V
120
15
100
80
10
60
, 40
20
3
X
3.0
4.
5.
6.
0.5
1.0
1.5
2.0
2.5
60
120
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