[ Calculus Archive ]

Review Questions for Section 3.9

1.

What number exceeds its square by the maximum amount?

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2.

A piece of wire 16 inches long is cut into two pieces. One piece is bent to form a square and the other is bent to form a circle. Where should the cut be made in order to minimize the total area of the square and circle?

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3.

An observatory is to be made in the form of a right circular cylinder surmounted by a hemispherical dome. If the hemispherical dome costs twice as much per square foot as the cylindrical wall, what are the most economical proportions for a given volume?

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4.

A merchant finds that he can sell 4,000 yards of a fabric each month if he prices it at $6.00 per yard, and that his monthly sales will increase by 250 yards for each $0.15 reduction in the price per yard. What price would yield the maximum revenue?

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• All the details