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An open box is to be made from a 16-inch by 30-inch piece of cardboard by...

An open box is to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest volume?

a. Draw and label the diagram that shows length x and width y of the box.

b. Find the volume formula in terms of x.

c. Find the x value for which the rectangle has maximum volume.

d. Use a limit to verify that the x value you found yields maximum volume.

e. Find the dimensions of the rectangle that will produce a maximum volume.

Math   Precalculus   
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