Questions from General Calculus


Q: Figure 12(b) shows an open rectangular box with a

Figure 12(b) shows an open rectangular box with a square base. Consider the problem of finding the values of x and h for which the volume is 32 cubic feet and the total surface area of the box is mini...

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Q: Find the slope of the tangent line to the curve y =

Find the slope of the tangent line to the curve y = (x2 - 15)6 at x = 4. Then write the equation of this tangent line.

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Q: Postal requirements specify that parcels must have length plus girth of at

Postal requirements specify that parcels must have length plus girth of at most 84 inches. Consider the problem of finding the dimensions of the square-ended rectangular package of greatest volume tha...

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Q: Consider the problem of finding the dimensions of the rectangular garden of

Consider the problem of finding the dimensions of the rectangular garden of area 100 square meters for which the amount of fencing needed to surround the garden is as small as possible. (a) Draw a pic...

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Q: A rectangular garden of area 75 square feet is to be surrounded

A rectangular garden of area 75 square feet is to be surrounded on three sides by a brick wall costing $10 per foot and on one side by a fence costing $5 per foot. Find the dimensions of the garden th...

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Q: A closed rectangular box with a square base and a volume of

A closed rectangular box with a square base and a volume of 12 cubic feet is to be constructed from two different types of materials. The top is made of a metal costing $2 per square foot and the rema...

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Q: Find the dimensions of the closed rectangular box with square base and

Find the dimensions of the closed rectangular box with square base and volume 8000 cubic centimeters that can be constructed with the least amount of material.

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Q: A canvas wind shelter for the beach has a back, two

A canvas wind shelter for the beach has a back, two square sides, and a top. Find the dimensions for which the volume will be 250 cubic feet and that requires the least possible amount of canvas.

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Q: A farmer has $1500 available to build an E-shaped

A farmer has $1500 available to build an E-shaped fence along a straight river so as to create two identical rectangular pastures. (See Fig. 13.) The materials for the side parallel to the river cost...

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Q: Find the dimensions of the rectangular garden of greatest area that can

Find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

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