t2(4) - Three sides of the enclosure will be built of...

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Methods of Calculus MAC3233 Test 2 February 23, 1996 Instructions: This is a closed-book, closed-notes test. Do not write your answers on this paper, use separate answer sheets. No calculators are allowed to be used. To receive credit, you must show all work . For the opti- mization problems, you are required to show why your answer is a minimum or maximum. The four problems are worth 25 points apiece. 1. f ( x ) = 1 3 x 3 - 3 x 2 + 20 (a) Give f 0 ( x ) and f 00 ( x ). (b) Find all relative extreme points. (c) Find all inflection points. (d) Sketch the graph. 2. f ( x ) = 8 x + 2 x - 4 (a) Give f 0 ( x ) and f 00 ( x ). (b) Find all relative extreme points. (c) Find all asymptotes. (d) Sketch the graph. 3. The owner of a shop plans to build a 168-square-foot rectangular enclosure on the store’s property in order to display some merchandise. The display area is to be located on the southwest corner of the store’s parking lot.
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Unformatted text preview: Three sides of the enclosure will be built of chain-link fencing, at a cost of $15 per running foot. The fourth side will be built of cement blocks, at a cost of $20 per running foot. The owner wants to minimize the total cost of building the enclosure. (a) Draw a picture, assigning variable names to the dimensions. (b) Give the objective equation. (c) Give the constraint equation. (d) Find the dimensions that minimize the costs. 4. A club oers memberships at the rate of $300 per person, provided that a minimum of 100 people join. For each member in excess of 100, the membership fee will be reduced $2 per person (for each member). How many memberships should the club try to sell in order to maximize its revenues? 1...
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