SOLUTION: Packaging. A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Equal-sized squares x inches on a side will be cut out of each corner, and then the e

Question 267042: Packaging. A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. 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
Volume
X V (x)
1
2
3
D) Plot the points in part (C) and sketch a graph of the volume function through these points. (c) a graphing utility can be used as an aid.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
A) Express the volume of the box V(x) in terms of x.
answer - - >
length = 12 - 2x
width = 8-2x
height = x
V(x) = (12-2x)(8-2x)(x)
--------
B) What is the domain of the function V ( determined by the physical restrictions)?
domain of the length: 0 <= x <= 6
domain of the width: 0 <= x <= 4
Of these two: 0 <= x < = 4
--------
C) Complete table
Volume
X . . . . . . . . . V (x)
1 . . . . . . . . . 60
2 . . . . . . . . . 64
3 . . . . . . . . . 36
---------
D) Plot the points in part (C) and sketch a graph of the volume function through these points. (c) a graphing utility can be used as an aid.
here is a graph:

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