Study Guide 2 F_13

# Find the absolute minimum value of the function f x

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Unformatted text preview: nimum (C) neither (A) absolute maximum (B) absolute minimum (C) neither (ii) x2 is a(n) (iii) x3 is a(n) (iv) x4 is a(n) 48. Find the absolute minimum value of the function f (x) = x3 + 2x2 − 4x + 12 over the interval [0, 2]. (Round to two decimal place as needed.) The absolute minimum occurs at (A) x = 0.00 (B) x = 0.67 (C) x = 1.79 (D) x = 2.00 (E) None of these 49. The number of cups of coﬀee sold at Lauren’s Coﬀee House for each week in November is shown in the graph below. Consider the closed interval [1, 5] and give the relative and absolute extrema for the interval. 50. The total proﬁt P (x) (in thousands of dollars) from the sale of x hundred thousand pillows is approximated by P (x) = −x3 + 12x2 + 60x − 300, for x ≥ 5. Find the number of pillows that must be sold to maximize proﬁt. The number of pillows is (A) less than 700,000 (B) between 700,000 and 900,000 (C) between 900,000 and 1,100,000 (D) between 1,100,000 and 1,300,000 (E) more than 1,300,000 51. Find the minimum value of the average cost for the cost function C (x) = x3 + 35x + 250 over the interval (0, 10]. The absolute minimum is (A) less than 105 (B) between 105 and 115 (D) between 125 and 135 (E) more than 135 (C) between 115 and 125 52. A hotel has 290 units. All rooms are occupied when the hotel charges \$90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs \$34 per day to service and maintain. What should the hotel charge per day in order to maximize daily proﬁt? (A) \$117 (B) \$192 (C) \$190 (D) \$207 (E) None of these 53. A baseball team is trying to determine what price to charge for tickets. At a price of \$18 per ticket, it averages 44,000 people per game. For every increase of \$1, it loses 1000 people. Every person at the game spends an average of \$8 on concessions. What price per ticket should be charged in order to maximize revenue? (A) \$27 (B) \$17 (C) \$13 (D) \$9 (E) None of these 54. If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where x p(x) = 164 − . 10 (i) Find an expression for the total revenue from the sale of x thousand candy bars. (ii) Find the value of x that leads to maximum revenue. (iii) Find the maximum revenue. 55. A local club is arranging a charter ﬂight to Hawaii. The cost of the trip is \$560 each for 80 passengers, with a refund of \$5 per passenger for each passenger in excess of 80. (i) Find the number of passengers that will maximize the revenue re...
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