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An open box is to be made from a flat piece of material 18 inches long and 5 inches wide by cutting equal squares
of length x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
V=
If we write the domain of the box as an open interval in the form (a,b), then what is a =?
And what is b =?
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After folding up the sides, the height of the box will be "x".
The length of the box will be (18-2x).
The width of the box will be (5-2x).
Hence, the volume of the box will be x*(18-2x)*(5-2x).
These inequalities should be in the place
18 - 2x > 0,
5 - 2x > 0,
that imply x < 2.5.
The domain of the volume function is {x| 0 < x < 2.5}, or, in the interval notation, (0,2.5).
Or a = 0, b = 2.5 inches.