An open box of maximum volume is to be made from square piece of material, s = 12 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). s-21 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 - 2(1) 1[12 - 2(1)]? = 100 2 12 - 2(2) 2[12 - 2(2)]? = 128 3 12 - 2(3) 3[12 - 2(3)]? = 12 - 2(4) 4[12 – 2(4)]2 = 4 5 12 - 2(5) 5[12 - 2(5)]2 = 6. 2(6) 6[12 - 2(6)]? = 12
An open box of maximum volume is to be made from square piece of material, s = 12 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). s-21 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 - 2(1) 1[12 - 2(1)]? = 100 2 12 - 2(2) 2[12 - 2(2)]? = 128 3 12 - 2(3) 3[12 - 2(3)]? = 12 - 2(4) 4[12 – 2(4)]2 = 4 5 12 - 2(5) 5[12 - 2(5)]2 = 6. 2(6) 6[12 - 2(6)]? = 12
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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Transcribed Image Text:Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
0 < x < 6
V=
(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
square piece of material, s = 12 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s-21
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
Height, x
Volume, V
12 - 2(1)
1[12 - 2(1)]? = 100
2
12 - 2(2)
2[12 - 2(2)]? = 128
3
12 - 2(3) 3[12 - 2(3)]? =
12 - 2(4) 4[12 – 2(4)]² =
4
5
12 - 2(5) 5[12 - 2(5)]2 =
6.
2(6) |6[12 - 2(6)]? =
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d32f8b7-96df-4b74-9062-e8549cafca0c%2F3da5da7f-27c2-4613-9b18-bf0cad30f106%2F1o4c34f_processed.png&w=3840&q=75)
Transcribed Image Text:An open box of maximum volume is to be made from
square piece of material, s = 12 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s-21
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
Height, x
Volume, V
12 - 2(1)
1[12 - 2(1)]? = 100
2
12 - 2(2)
2[12 - 2(2)]? = 128
3
12 - 2(3) 3[12 - 2(3)]? =
12 - 2(4) 4[12 – 2(4)]² =
4
5
12 - 2(5) 5[12 - 2(5)]2 =
6.
2(6) |6[12 - 2(6)]? =
12
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