Packaging. Refer to Problem 1.
(A) Table 1 shows the volume of the box for some values of x between 1 and 2. Use these values to estimate to one decimal place the value of x between 1 and 2 that would produce a box with a volume of 65 cu in.
Table 1 Volume
x
V(x )
1.1
62.524
1.2
64.512
1.3
65.988
1.4
66.976
1.5
67.5
1.6
67.584
1.7
67.252
(B) Describe how you could refine this table to estimate x to two decimal places.
(C) Carry out the refinement you described in part (B) and approximate x to two decimal places.
Problem 1
Packaging. A candy box will be made out of a piece of cardboard that measures 8 by 12 in. Equal-sized squares x inches on a side will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box.
(A) Express the volume of the box V(x) in terms of x.
(B) What is the domain of the function v (determined by the physical restrictions)?
(C) Complete Table 2.
Table 2 Volume
x
V(x)
1
2
3
(D) Plot the points in part (C) and sketch a graph of the volume function using these points.
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