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t2(1) - identical rectangular pastures The materials for...

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Methods of Calculus MAC3233 Test 2 Feb. 24, 1993 Instructions: Do not write your answers on this paper, use separate answer sheets. This is a closed-book test. No calculators are allowed to be used. 25 points each. (1) f ( x ) = 12 x + x 3 - 1 (a) f 0 ( x ) = ? f 00 ( x ) = ? (b) Find all asymptotes. (c) Find all local extrema and inflection points. (d) Sketch the graph. (2) A one-product firm estimates that its daily cost function (in suitable units) is C ( x ) = x 3 - 7 x 2 + 13 x + 15 and its demand equation is p = 28 - x . (a) Write the formula for the daily profit function P ( x ). (b) Find the value of x that maximizes the daily profit. (3) A farmer has $3000 available to build an E-shaped fence along a straight river so as to create 2
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Unformatted text preview: identical rectangular pastures. The materials for the side parallel to the river cost $6 per foot and the materials for the 3 sections perpendicular to the river cost $5 per foot. Find the dimensions for which the total pasture area is as large as possible. (4) A club offers memberships at the rate of $300, provided that a minimum of 150 people join. For each member in excess of 150, the membership fee will be reduced by $2 per person (for all members). How many memberships should be sold to maximize the club’s revenue? 1...
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