An open box is to be constructed from a piece of cardboard 10 cm by 20 cmlength x from each corner and folding up the sides, as shown in the figure.

(a) Express the volume V of the box as a function of x.

The dimensions of the box are 20 - 2x, 10 - 2x, and x.

V(x) = x(10 - 2x) (20 - 2x) - answer to a)

Since all the dimensions must be positive, the domain is 0 < x < 5. - answer to b)

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