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t4(4)

# t4(4) - t is in years t = 0 corresponds to 1987 If R t = 17...

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MAC3233 Test 4 April 15, 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 . Some numerical answers may involve the function ln or the number e . You are not required to simplify your answers. 1. (10 points) Find f 0 ( x ), if f ( x ) = ln( x 3 + 2) 2. (15 points) f ( x ) = 2 x + 3 e - x . (a) f 0 ( x ) = ? (b) f 00 ( x ) = ? (c) Find the x coordinate of each possible extremum. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum. 3. (15 points) f ( x ) = 15 x - 7 x ln x . (a) f 0 ( x ) = ? (b) f 00 ( x ) = ? (c) Find the x coordinate of each possible extremum. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum. 4. (15 points) The rate of production of a certain commodity changes from year to year. Suppose that since 1987 the rate of production is given by the function R ( t ), where R is in units per year and
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Unformatted text preview: t is in years ( t = 0 corresponds to 1987). If R ( t ) = 17 . 04 e . 016 t , ﬁnd the formula for A ( t ), the total amount of the commodity produced from 1987, as a function of t . 5. (10 points each) Solve each of the following. (a) Z 35 e-9 x dx (b) Z 5 x-2 dx (c) Z 5 2 ( x 3 + 5 x-3) dx 6. (15 points) A local bakery wants to know how much it costs to keep a machine running in their shop. Taken into consideration are all expenses associated to owning and operating the machine, including depreciation due to wear and tear and necessary maintenance costs. Suppose that for a machine which has been in service for t months, expenses cost the company a rate of t 2-4 t + 250 dollars per month. If a machine has been in service for 15 months, ﬁnd the total expenses of keeping it running for an additional 9 months. 1...
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