Packaging. Refer to Problem 1.(A) Table 1 shows the volume of the box for some values of x...

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

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(B) Describe how you could refine this table to estimate x to two decimal places.

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(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.

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(B) What is the domain of the function v (determined by the physical restrictions)?

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(C) Complete Table 2.

Table 2 Volume

x	V(x)
1
2
3

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(D) Plot the points in part (C) and sketch a graph of the volume function using these points.