# Trouble Understanding Elementary Functions.

Here's an other question that I am having trouble with.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. By cutting out equal squares of side at each corner and then folding up the sides as in the figure. How do I express the volume $V$ of the box as a function of $x$.

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You should be able to see that the height of the box is $x$. The width of the box is 20-?... And the depth is 12-?... – David Mitra Dec 25 '11 at 16:27

Well what's the formula for the volume $V$? It's length times width times height. Now the height in your question is $x$, the length is $20 - 2x$.

Can you guess what the width is and do it from here?

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wait a minute.You say length = $20 - 2x$.The reason being we are cutting off $x$,how come it's $20 - 2x$ and not $20 - x$? – alok Dec 25 '11 at 16:49
@alok: That's because you're cutting of $x$ once on each side, so in total you cut it off twice. – Rudy the Reindeer Dec 25 '11 at 16:54
To be fully correct you should also include the upper and lower bounds on the possible values of x. – David Marquis Dec 25 '11 at 18:35