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Question 360564: An open box is to be made from a square piece of material 36cm on a side by cutting equal squares from the corners and turning up the sides. See the following table:
Height Width Volume
1 36- 2(1) 1[36-2(1)]^2 =1156
2 36- 2(2) 2[36-2(2)]^2 =2048
1. Verify that the volume of the box is given by V = x(36-2x)^2. Determine the domain of the function.
2. Use a graphing calculator to graph V, and use the range of dimensions from the table to find the x- value for which V(x) is maximum.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Verify that the volume of the box is given by V = x(36-2x)^2. Determine the domain of the function.
height = x
base is 36-2x by 36-2x
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Domain:
Solve: 36-2x >= 0
2x <= 36
0<= x <= 18
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2. Use a graphing calculator to graph V, and use the range of dimensions from the table to find the x- value for which V(x) is maximum.
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Maximum when x = 6
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Cheers,
Stan H.
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