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【段考】高三國文
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無年度 - Ⅵ基礎評量:國文(第十一回蘭亭集序)#108277
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1. City and Country Cycles finds that if it sells x racing bicycles per month, it’s costs will be C(x) = 20x+72,000 and its revenue will be R( x ) = −3 x 2 + 1,800 x (both in dollars). a. Find the store’s break-even points. b. Find the number of bicycles that will maximize profit, and the maximum profit.
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2. If a person’s temperature after x hours of strenuous exercise is T (x ) = x 3 (4 − x 2 ) + 98.6 degrees Fahrenheit (for 0 ≤ x ≤ 2 ), find the rate of change of the temperature after 1 hour.
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3. Based on a recent study, the “happiness” of people who live in a country whose average temperature is t degrees Fahrenheit is given by h(t ) = 8.2 − (0.01t − 2.8) 2 , for 35 ≤ t ≤ 72 (“Happiness” was rated from 1 = “not at all happy” to 4 “very happy”.) Find h (40) and h ' (40) . Interpret your answer.
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4. A politician estimates that by campaigning in a country for x days, she will gain 2x (thousand) votes, but her campaign expenses will be 5 x 2 + 500 dollars. She wants to campaign for the number of days 2x that maximizes the number of votes per dollar, f ( x) = . For how many days should shcampaign?
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