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Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. Estimate the intervals of increase and decrease and intervals of concavity, and use calculus to find these intervals exactly.

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Q: Two vertical poles PQ and ST are secured by a rope PRS

Two vertical poles PQ and ST are secured by a rope PRS going from the top of the first pole to a point R on the ground between the poles and then to the top of the second pole as in the figure. Show t...

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Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. In particular, you should use graphs of f' and f" to estimate the intervals of increase and decrease, extreme values, intervals...

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Q: The frame for a kite is to be made from six pieces

The frame for a kite is to be made from six pieces of wood. The four exterior pieces have been cut with the lengths indicated in the figure. To maximize the area of the kite, how long should the diago...

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Q: Find the dimensions of a rectangle with perimeter 100 m whose area

Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.

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Q: Let and be positive numbers. Find the length of the shortest

Let and be positive numbers. Find the length of the shortest line segment that is cut off by the first quadrant and passes through the point (a, b).

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Q: The manager of a 100-unit apartment complex knows from experience

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $800 per month. A market survey suggests that, on average, one additional unit will rem...

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Q: A manufacturer has been selling 1000 television sets a week at $

A manufacturer has been selling 1000 television sets a week at $450 each. A market survey indicates that for each $10 rebate offered to the buyer, the number of sets sold will increase by 100 per week...

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Q: During the summer months Terry makes and sells necklaces on the beach

During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for @10 each and his sales averaged 20 per day. When he increased the price by $1, he found tha...

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Q: A baseball team plays in a stadium that holds 55,000

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at $10, the average attendance had been 27,000. When ticket prices were lowered to $8, the average attendance rose t...

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