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mathematics
college mathematics for business
Questions and Answers of
College Mathematics For Business
In Problem find the absolute maximum and absolute minimum of each function on the indicated intervals.f(x) = 100 - x2(A) [-10, 10] (B) [0, 10] (C) [10, 11]
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f.f(x) = 8x3 - 2x4
In Problem find the absolute maximum and absolute minimum of each function on the given interval.f(x) = e-x on [-1, 1]
In Problem find the indicated derivative for each function.y″ for y = (x2 + 9)4
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f.f(x) = (x - 1)3 (x + 3)
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) x - 2
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f. 3x f(x) : х + 2
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f. f(x) : x? + 27
A deli sells 640 sandwiches per day at a price of $8 each.(A) A market survey shows that for every $0.10 reduction in price, 40 more sandwiches will be sold. How much should the deli charge for a
In Problem find the absolute maximum and absolute minimum of each function on the given interval.f(x) = 9 - x2 on [-4, 4]
In Problem find the x and y coordinates of all inflection points.f(x) = x3 + 30x2
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f. f(x) (x + 2)?
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = 5 + 5e-0.1x
A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f. x f(x) .2 х* + 3
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = x2 - 4x + 4
In Problem find the x and y coordinates of all inflection points.f(x) = x5/3 + 2
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f.f(x) = x3 - 12x + 8
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = x2 + 2x + 1
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f.f(x) = x3 - 27x + 30
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = 5xe-0.2x
A commercial cherry grower estimates from past records that if 30 trees are planted per acre, then each tree will yield an average of 50 pounds of cherries per season. If, for each additional tree
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f.f(x) = 5 - 5e-x
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = -x2 - 2x + 5
In Problem find the x and y coordinates of all inflection points.f(x) = 1 + x + x2/5
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f. 6. f(x) x + 2
In Problem summarize all the pertinent information obtained by applying the final version of the graphing strategy and sketch the graph of f.f(x) = x3 ln x
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f. 5 f(x) x - 4
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = -x2 + 6x + 1
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = ln(1 - x)
A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a
Find each limit in Problem ear - 1 lim 3x
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = x3 - 3
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = x4 - 24x2
In Problem find (A) f′(x)(B) The partition numbers for f′(C) The critical numbers of f.f(x) = x1/3
Find each limit in Problem x2 - 5x + 6 lim x2 x + x - 6
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = 6 - x3
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = 3x4 - 18x2
Find each limit in Problem In (1 + x) lim x2
A fence is to be built to enclose a rectangular area of 800 square feet. The fence along three sides is to be made of material that costs $6 per foot. The material for the fourth side costs $18 per
Find each limit in Problem In (1 + x) lim x>0 1 + x
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = x4 - 7
In Problem find the absolute extremum, if any, given by the second derivative test for each function.f(x) = 8 - x4
In Problem summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) 2 - 4
In Problem explain why L’Hôpital’s rule does not apply. If the limit exists, find it by other means. x + 2 lim (x - 2)4
Find each limit in Problem etr lim .2 4x
In Problem find the absolute extremum, if any, given by the second derivative test for each function. 4 f(x) = x +
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = -x4 + 12x3
Find each limit in Problem et + e* - 2 lim x2
In Problem find the absolute extremum, if any, given by the second derivative test for each function. 9. f(x) = x + -
Find each limit in Problem V1 + x - 1 lim
In Problem find the absolute extremum, if any, given by the second derivative test for each function. -3 f(x) x² + 2
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plant for production of the primer.
In Problem find the absolute extremum, if any, given by the second derivative test for each function. 2 f(x) x? + 3
Find each limit in Problem In x lim
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = ln (x2 +
In Problem find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = x3 + 5x + 2
Find each limit in Problem In (1 + 6x) lim In (1 +3x)
In Problem find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x, y coordinates of the inflection points.f(x) = ln (x2 -
In Problem find the absolute extremum, if any, given by the second derivative test for each function. 1 - x f(x) x? - 4
A publishing company sells 50,000 copies of a certain book each year. It costs the company $1 to store a book for one year. Each time that it prints additional copies, it costs the company $1,000 to
Find each limit in Problem In (1 + 6x) lim x0 In (1 + 3x)
In Problem find the absolute extremum, if any, given by the second derivative test for each function. X - 1 f(x) x2 - 1
A tool company has a uniform annual demand for 9,000 premium chainsaws. It costs $5 to store a chainsaw for a year and $2,500 to set up the plant for manufacture of the premium model. How many
In Problem find the absolute extremum, if any, given by the second derivative test for each function. f(x) x? + 4
Refer to the above graph of y = f′(x). Which of the following could be the graph of y = f″(x)? f"(x) f"(x) (A) (B) -5 -5 5 f"(x) (C) -5 5
The cost per hour for fuel to drive a rental truck from Chicago to New York, a distance of 800 miles, is given byf(v) = 0.03v2 - 2.2v + 72where v is the speed of the truck in miles per hour. Other
In Problem find the absolute extremum, if any, given by the second derivative test for each function. x? f(x) .2 + 1
A freshwater pipeline is to be run from a source on the edge of a lake to a small resort community on an island 5 miles offshore, as indicated in the figure.(A) If it costs 1.4 times as much to lay
Use the second-derivative test to find any local extrema forf(x) = x3 - 6x2 - 15x + 12
Find the absolute minimum, if it exists, for 16 y = f(x) = x + .2 x> 0
In Problem find the indicated extremum of each function on the given interval.Absolute minimum value on (0, ∞) forf(x) = 2x2 - 8x + 6
Find the absolute maximum and absolute minimum, if either exists, fory = f(x) = x3 - 12x + 12 -3 ≤ x ≤ 5
A lake used for recreational swimming is treated periodically to control harmful bacteria growth. Suppose that t days after a treatment, the concentration of bacteria per cubic centimeter is given
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) forf(x) = 3x2 - x3
Find the absolute maximum, if it exists, forf(x) = 11x - 2x ln x x > 0
If it is known from past experiments that the height (in feet) of a certain plant after t months is given approximately byH(t) = 4t1/2 - 2t 0 ≤ t ≤ 2then how long, on average, will it take a
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) for 12 f(x) 3D 20- 3х
Find the absolute maximum, if it exists, forf(x) = 10xe-2x x > 0
In Problem find the indicated extremum of each function on the given interval.Absolute minimum value on (0, ∞) forf(x) = (x + 4) (x - 2)2
In a newly incorporated city, the voting population (in thousands) is estimated to beN(t) = 30 + 12t2 - t3 0 ≤ t ≤ 8where t is time in years. When will the rate of increase of N(t) be most rapid?
In Problem find the indicated extremum of each function on the given interval.Absolute minimum value on (0, ∞) for 64 f(x) = 10 + 2x + .2
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) forf(x) = 2x4 - 8x3
In Problem apply the graphing strategy and summarize the pertinent information. Round any approximate values to two decimal places.f(x) = x4 + x3 - 4x2 - 3x + 4
In Problem find the indicated extremum of each function on the given interval.Absolute minimum value on (0, ∞) for 1 f(x) = x + - 30 +
In Problem apply the graphing strategy and summarize the pertinent information. Round any approximate values to two decimal places.f(x) = 0.25x4 - 5x3 + 31x2 - 70x
The graph in the figure approximates the rate of change of the price of tomatoes over a 60-month period, where p(t) is the price of a pound of tomatoes and t is time (in months).(A) Write a brief
Find the absolute maximum, if it exists, for In x x > 0 et f(x)
Find the absolute maximum, if it exists, forf(x) = 3x - x2 + e-x x > 0
In Problem find the indicated extremum of each function on the given interval.Absolute minimum value on (0, ∞) for at f(x) %3D .2
A company manufactures and sells x e-book readers per month. The monthly cost and price–demand equations are, respectively,C(x) = 350x + 50,000p = 500 - 0.025x 0 ≤ x ≤ 20,000(A) Find the
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) for f(x) et
A fence is to be built to enclose a rectangular area. The fence along three sides is to be made of material that costs $5 per foot. The material for the fourth side costs $15 per foot.(A) If the area
A 200-room hotel in Reno is filled to capacity every night at a rate of $40 per room. For each $1 increase in the nightly rate, 4 fewer rooms are rented. If each rented room costs $8 a day to
A computer store sells 7,200 boxes of storage drives annually. It costs the store $0.20 to store a box of drives for one year. Each time it reorders drives, the store must pay a $5.00 service charge
The data in the table show the daily demand x for cream puffs at a state fair at various price levels p. If it costs $1 to make a cream puff, use logarithmic regression (p = a + b ln x) to find the
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) forf(x) = 5x - 2x ln x
The total cost of producing x dorm refrigerators per day is given byC(x) = 4,000 + 10x + 0.1x2Find the minimum average cost. Graph the average cost and the marginal cost functions on the same
The cost of producing x wheeled picnic coolers is given byC(x) = 200 + 50x - 50 ln x x ≥ 1Find the minimum average cost.
In Problem find the indicated extremum of each function on the given interval.Absolute maximum value on (0, ∞) forf(x) = x2 (3 - ln x)
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