(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 200 150 100 50 V 400 300 200 100 2 2 4 4 6 6 8 8 X 50 40 30 20 10 V 400 300 200 100 1 2 2 4 3 6 4 8 X X
(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 200 150 100 50 V 400 300 200 100 2 2 4 4 6 6 8 8 X 50 40 30 20 10 V 400 300 200 100 1 2 2 4 3 6 4 8 X X
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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Chapter4: Calculating The Derivative
Section4.1: Techniques For Finding Derivatives
Problem 64E: Dogs Human Age From the data printed in the following table from the Minneapolis Star Tribune on...
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Calculus 1 Optimization
Transcribed Image Text:(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
V
200
150
100
50
400
300
200
100
2
2
4
6
6
8
8
X
X
50
40
30
20
10
400
300
200
100
1
2
2
4
3
6
4
8
X
X
![An open box of maximum volume is to be made from a square piece of material, s = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s - 2x
X
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
18 - 2(1)
18 - 2(2)
182(3)
3[18 – 2(3)]² =
182(4) 4[18 – 2(4)]² =
182(5) 5[18 — 2(5)]² =
182(6) 6[18 – 2(6)]² =
V =
Height, x
1
2
3
4
5
s-2x-
6
Use the table to guess the maximum volume.
V =
Volume, V
1[182(1)]²= 256
2[182(2)]² = 392
(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 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f24281c-25ef-4ab9-a2c5-64dee6059ac4%2F880a5f60-fdcc-4af1-b832-5eb514395d36%2Fe9q1p7d_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 = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
s - 2x
X
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Length and
Width
18 - 2(1)
18 - 2(2)
182(3)
3[18 – 2(3)]² =
182(4) 4[18 – 2(4)]² =
182(5) 5[18 — 2(5)]² =
182(6) 6[18 – 2(6)]² =
V =
Height, x
1
2
3
4
5
s-2x-
6
Use the table to guess the maximum volume.
V =
Volume, V
1[182(1)]²= 256
2[182(2)]² = 392
(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 =
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