An open box of maximum volume is to be made from a square piece of material, s = 18 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 18 - 2(1) 1[18 - 2(1)]2 = 256 18 - 2(2) 2[18 - 2(2)]2 = 392 2 18 - 2(3) 3[18 - 2(3)]2 =| 3 18 - 2(4) 4[18 - 2(4)]2 = 4 18 - 2(5) 5[18 - 2(5)]2 = | 18 - 2(6) 6[18 - 2(6)]2 = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0 < x< 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =

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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(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
V
V
200
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100
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V
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Transcribed Image Text:(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 200 50 40 150 30 100 20 50 10 2 4 6 8 1 4 V V 400 400 300 300 200 200 100아 100아 2 4 6. 8 2 4 6 8
An open box of maximum volume is to be made from a square piece of material, s = 1
centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s- 2.
(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
18 - 2(1)
1[18 - 2(1)]2 = 256
1
18 - 2(2)
2[18 - 2(2)]? = 392
2
18 - 2(3) 3[18 - 2(3)]2 =
3
18 - 2(4) 4[18 - 2(4)]2 =
4
18 - 2(5) 5[18 - 2(5)]2 = |
18 - 2(6)
6[18 - 2(6)]? = [
6
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
V =
0 <x< 9
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s = 1 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). s- 2. (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 18 - 2(1) 1[18 - 2(1)]2 = 256 1 18 - 2(2) 2[18 - 2(2)]? = 392 2 18 - 2(3) 3[18 - 2(3)]2 = 3 18 - 2(4) 4[18 - 2(4)]2 = 4 18 - 2(5) 5[18 - 2(5)]2 = | 18 - 2(6) 6[18 - 2(6)]? = [ 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 <x< 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
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