How can I get the result?
Which is the result?
![An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the
coners and turning up the sides (see figure).
S-2r
X
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Height, xLength and
Width
Volume, V
12 2(1)
1
1[12 2(1)12
2[12 2(2)12
= 100
12 2(2)
2.
= 128
3[12 2(3)12
12 2(3)
3
12 2(4) 4[12 2(4)]2
4
12 2(5) 5[12 2(5)]2
12 2(6) 6[12 2(6)]2
Use the table to quess the maximum volume.
=A
(b) Write the volume Vas a function of x.
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
graphing 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
X
2
4
5
6
X
0.5
1.0
1.5
2.0
2.5
3.0
V
V
60
120
50
100
40
80
30
60
20
40
10
20
X
6
1
X
2
3
4
5
3
5
2
S 2r](https://content.bartleby.com/qna-images/question/0291f6f9-8c73-44e5-9b62-f3f476a1e310/24b85acc-632b-4f9c-9ddc-cb3dc9c2177d/8ztmbg8.jpeg)
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