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Deck 4: Techniques of Differentiation With Applications
Full screen (f)
Question
Find the slope of the tangent to the graph of the given function at the indicated point. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the following derivative. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the slope of the tangent to the graph of the given function 
at the indicated point 
.
A)
B)
C)
D)
E)
at the indicated point .A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find all the values of x (if any)where the tangent line to the graph of the given equation is horizontal. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If a stone is dropped from a height of 300 feet, its height s after t seconds is given by 
with s in feet. a. Find the stone s velocity at 
seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.
A)-100, 1.94, -77.46
B)-10, 3.87, -600.00
C)-200, 15.00, -600.00
D)200, 3.87, -154.92
E)-200, 3.87, -154.92
with s in feet. a. Find the stone s velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.A)-100, 1.94, -77.46
B)-10, 3.87, -600.00
C)-200, 15.00, -600.00
D)200, 3.87, -154.92
E)-200, 3.87, -154.92
Question
Given. 
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, 7
B)yes, 7
C)no, 0
D)yes, 5
E)yes, 0
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.A)no, 7
B)yes, 7
C)no, 0
D)yes, 5
E)yes, 0
Question
For the cost function, find the marginal cost at the given production level x . 
A)$5.00 per item
B)$5.20 per item
C)$4.80 per item
D)$4.81 per item
E)$4.78 per item
A)$5.00 per item
B)$5.20 per item
C)$4.80 per item
D)$4.81 per item
E)$4.78 per item
Question
Evaluate the following derivative. 
Question
Find the slope of the tangent to the graph of the given function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Given. 
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________ Question
Use the shortcut rules to calculate the derivative of the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
Question
Given. 
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________ Question
The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption (in milliliters per hour)can be approximated by 
where t is the time (in days)since the egg was laid. (An egg will typically hatch at around 
.)Find 
.
A)
B)
C)
D)
E)
where t is the time (in days)since the egg was laid. (An egg will typically hatch at around .)Find .A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
Question
Given. 
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, -5
B)no, -12
C)yes, 12
D)yes, -5
E)no, 5
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.A)no, -5
B)no, -12
C)yes, 12
D)yes, -5
E)no, 5
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
For the cost function C ( x ), find the marginal cost at the given production level x . 
A)$39.96 per item
B)$49.95 per item
C)$49.97 per item
D)$51.25 per item
E)$40.00 per item
A)$39.96 per item
B)$49.95 per item
C)$49.97 per item
D)$51.25 per item
E)$40.00 per item
Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: 
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. Government clean-air subsidies to the firm are based on the formula 
where q is again the reduction in emissions (in pounds per day)and S is the subsidy (in dollars). Calculate the net cost function 
given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost?
A)q = $2, N ( q )= $2,300
B)q = $4, N ( q )= $2,300
C)q = $2, N ( q )= $4,600
D)q = $2.5, N ( q )= $2,375
E)q = $2.5, N ( q )= $2,300
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. Government clean-air subsidies to the firm are based on the formula where q is again the reduction in emissions (in pounds per day)and S is the subsidy (in dollars). Calculate the net cost function given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost?A)q = $2, N ( q )= $2,300
B)q = $4, N ( q )= $2,300
C)q = $2, N ( q )= $4,600
D)q = $2.5, N ( q )= $2,375
E)q = $2.5, N ( q )= $2,300
Question
Your company is planning to air a number of television commercials during the ABC television network s presentation of the Academy Awards. ABC is charging your company $795,000 per 30-second spot. Additional fixed costs (development and personnel costs)amount to $400,000, and the network has agreed to provide a discount of 
for x television spots. Compute marginal cost 
and average cost 
.
A)
B)
C)
D)
E)
for x television spots. Compute marginal cost and average cost .A)
B)
C)
D)
E)
Question
The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula 
. Evaluate the average cost 
.
A)$32.00
B)$29.50
C)$28.00
D)$3,249.50
E)$3,200.00
. Evaluate the average cost .A)$32.00
B)$29.50
C)$28.00
D)$3,249.50
E)$3,200.00
Question
Assume that the demand function for tuna in a small coastal town is given by 
where p is the price (in dollars)per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in 1 month. Calculate the price that the town s fishery should charge for tuna in order to produce a demand of 625 pounds of tuna per month.
A)$1
B)$32
C)$1,200
D)$800
E)$2
where p is the price (in dollars)per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in 1 month. Calculate the price that the town s fishery should charge for tuna in order to produce a demand of 625 pounds of tuna per month.A)$1
B)$32
C)$1,200
D)$800
E)$2
Question
The cost, in thousands of dollars, of airing x television commercials during a Super Bowl game is given by the formula 
. Estimate how fast (in dollars per television commercial)the cost is going up when x = 8.
A)$1,500
B)$1,500,032
C)$1,500,0
D)$1,499,984
E)$1,499,968
. Estimate how fast (in dollars per television commercial)the cost is going up when x = 8.A)$1,500
B)$1,500,032
C)$1,500,0
D)$1,499,984
E)$1,499,968
Question
Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that 
. Find M (30), M (70)and M (95).
A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049
. Find M (30), M (70)and M (95).A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049
Question
Find the value of x for which the marginal profit is zero. 
A)x = -5,000
B)x = 10,000
C)x = 5,000
D)x = 7,000
E)x = 2,500
A)x = -5,000
B)x = 10,000
C)x = 5,000
D)x = 7,000
E)x = 2,500
Question
The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: 
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?
A)$1,400
B)$2,800
C)$7,800
D)$2,100
E)$700
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?A)$1,400
B)$2,800
C)$7,800
D)$2,100
E)$700
Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
Calculate 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The estimated marginal revenue for sales of ESU soccer team T-shirts is given by 
where p is the price (in dollars)the soccer player charge for each shirt. Find R (1), R (5), R (8). Select the correct answer rounded to four decimal places.
A)R '(5)= 0.0049, R '(8)= 0, R '(1)= -3.9987
B)R '(1)= 3.9987, R '(5)= -0.0049, R '(8)= 0
C)R '(1)= -3.9987, R '(5)= 0, R '(8)= -0.0049
D)R '(1)= 0.0049, R '(5)= 0, R '(8)= -3.9987
E)R '(5)= 0.0049, R '(1)= 0, R '(8)= -3.9987
where p is the price (in dollars)the soccer player charge for each shirt. Find R (1), R (5), R (8). Select the correct answer rounded to four decimal places.A)R '(5)= 0.0049, R '(8)= 0, R '(1)= -3.9987
B)R '(1)= 3.9987, R '(5)= -0.0049, R '(8)= 0
C)R '(1)= -3.9987, R '(5)= 0, R '(8)= -0.0049
D)R '(1)= 0.0049, R '(5)= 0, R '(8)= -3.9987
E)R '(5)= 0.0049, R '(1)= 0, R '(8)= -3.9987
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Calculate 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
According to the equation given, a toy manufacturer calculates its daily profit P (in dollars)based on the number of workers n it employs. 
Calculate the marginal product at an employment level of 100 workers.
A)$39,960
B)$36,000
C)$3,999,960
D)$320
E)$440
Calculate the marginal product at an employment level of 100 workers.A)$39,960
B)$36,000
C)$3,999,960
D)$320
E)$440
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Your monthly profit (in dollars)from selling magazines is given by 
where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.
A)P (100)= $215, P '(100)= $2.08
B)P (100)= $430, P '(100)= $4.15
C)P (100)= $417.32, P '(100)= $0.35
D)P (100)= $417.32, P '(100)= $4.15
E)P (100)= $860, P '(100)= $4.65
where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.A)P (100)= $215, P '(100)= $2.08
B)P (100)= $430, P '(100)= $4.15
C)P (100)= $417.32, P '(100)= $0.35
D)P (100)= $417.32, P '(100)= $4.15
E)P (100)= $860, P '(100)= $4.65
Question
The monthly sales of Sunny Electronics new stereo system is given by 
hundred units per month, 
months after its introduction. The price Sunny charges is 
dollars per stereo system, 
months after its introduction. The revenue Sunny earns then must be 
. Find the rate of change of revenue 
months after introduction. Please enter your answer in dollars/month without the units.
hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction. Please enter your answer in dollars/month without the units. Question
Find the equation of the line tangent to the graph of the given function at the point 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The Verhulst model for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula: 
where p is the total population in thousands of organisms, 
and 
are constants that depend on the particular circumstances and organism being studied, and 
is the reproduction rate in thousands of organisms per hour. If 
and 
, find 
.
A)
B)
C)
D)
E)
where p is the total population in thousands of organisms, and are constants that depend on the particular circumstances and organism being studied, and is the reproduction rate in thousands of organisms per hour. If and , find .A)
B)
C)
D)
E)
Question
Find the equation of the line tangent to the graph of the given function at the point with 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by 
dollars after 
months. After 
months, the company had 
passengers per month. How fast was its cost per passenger changing after 
months?
A)$0.39 per month
B)$0.01 per month
C)-$0.18 per month
D)$0.29 per month
E)$0.10 per month
dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months?A)$0.39 per month
B)$0.01 per month
C)-$0.18 per month
D)$0.29 per month
E)$0.10 per month
Question
Compute the indicated derivative using the chain rule. 
A)-4
B)8
C)
D)-2
E)
A)-4
B)8
C)
D)-2
E)
Question
Your Porche s gas mileage (in miles per gallon)is given as a function 
of speed 
in miles per hour. 
Calculate 
.
A)
B)
C)
D)
E)
of speed in miles per hour. Calculate .A)
B)
C)
D)
E)
Question
Calculate the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the indicated derivative. 
Please round the answer to the nearest hundredth.
A)
B)
C)
D)
E)
Please round the answer to the nearest hundredth.A)
B)
C)
D)
E)
Question
The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by 
dollars after 
months. After 
months, the company had 
passengers per month. How fast was its cost per passenger changing after 
months? Enter your answer in dollars/month rounded to the nearest cent and without the units.
dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months? Enter your answer in dollars/month rounded to the nearest cent and without the units. Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
Compute the derivative. 
A)92
B)36
C)59
D)72
E)78
A)92
B)36
C)59
D)72
E)78
Question
Compute the derivative. 
A)9
B)5
C)3
D)0
E)1
A)9
B)5
C)3
D)0
E)1
Question
Find the indicated derivative. 
Please round the answer to the nearest hundredth.
A)
B)
C)
D)
E)
Please round the answer to the nearest hundredth.A)
B)
C)
D)
E)
Question
The monthly sales of Sunny Electronics new stereo system is given by 
hundred units per month, 
months after its introduction. The price Sunny charges is 
dollars per stereo system, 
months after its introduction. The revenue Sunny earns then must be 
. Find the rate of change of revenue 
months after introduction.
A)-$473,000 per month
B)-$567,500 per month
C)$31,840 per month
D)$318,400 per month
E)$197,600 per month
hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction.A)-$473,000 per month
B)-$567,500 per month
C)$31,840 per month
D)$318,400 per month
E)$197,600 per month
Question
Calculate 
. You need not expand your answer. 
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Question
Find the equation of the line tangent to the graph of the given function at the point 
. 
. Question
Find the indicated derivative. The independent variable is a function of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Calculate the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Compute the indicated derivative using the chain rule. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
The soap bubble I am blowing has a radius that is growing at a rate of 9 cm/s. How fast is the surface area growing when the radius is 14 cm? (The surface area of a sphere of radius r is 
.)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
Find the derivative of the following function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
The Pentagon is planning to build a new satellite that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.5 foot/week. Its cost will be $1,000 per cubic foot. At the point when the plans call for a satellite 5 feet in radius, how fast is the cost growing? (The volume of a solid sphere of radius r is 
.)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
Compute the indicated derivative using the chain rule. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 6 miles. (The area of a disc of radius r is 
.)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
Question
Match between columns
Question
Find the equation of the tangent line for 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.4 cm/day. How fast is the area growing when the culture is 3 centimeters in radius? (The area of a disc of radius r is 
.)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
Question
Calculate the derivative of the function. 
Please enter your answer as an expression.
Please enter your answer as an expression. Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Calculate the derivative of the function. 
Question
Find the derivative of the following function. 
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by 
where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute 
at a production level of 24,000 CDs per day and 
.
where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 24,000 CDs per day and . Question
The demand for the Cyberpunk II arcade video game is modeled by the logistic curve 
where q ( t )is the total number of units sold t months after the game s introduction. Use technology to estimate 
. Assume that the manufacturers of Cyberpunk II sell each unit for $600. What is the company s marginal revenue, 
? Use the chain rule to estimate the rate at which revenue is growing 5 months after the introduction of the video game. Please round each answer to the nearest whole number.
A)
B)
C)
D)
E)
where q ( t )is the total number of units sold t months after the game s introduction. Use technology to estimate . Assume that the manufacturers of Cyberpunk II sell each unit for $600. What is the company s marginal revenue, ? Use the chain rule to estimate the rate at which revenue is growing 5 months after the introduction of the video game. Please round each answer to the nearest whole number.A)
B)
C)
D)
E)
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Deck 4: Techniques of Differentiation With Applications
1
Find the slope of the tangent to the graph of the given function at the indicated point.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Evaluate the following derivative.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find the slope of the tangent to the graph of the given function at the indicated point .
A)
B)
C)
D)
E)
at the indicated point .A)
B)
C)
D)
E)
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5
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Find all the values of x (if any)where the tangent line to the graph of the given equation is horizontal.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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7
If a stone is dropped from a height of 300 feet, its height s after t seconds is given by with s in feet. a. Find the stone s velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.
A)-100, 1.94, -77.46
B)-10, 3.87, -600.00
C)-200, 15.00, -600.00
D)200, 3.87, -154.92
E)-200, 3.87, -154.92
with s in feet. a. Find the stone s velocity at seconds. b. When does it reach the ground, and how fast is it travelling when it hits the ground? Round your answers to the nearest hundredth.A)-100, 1.94, -77.46
B)-10, 3.87, -600.00
C)-200, 15.00, -600.00
D)200, 3.87, -154.92
E)-200, 3.87, -154.92
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8
Given. Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, 7
B)yes, 7
C)no, 0
D)yes, 5
E)yes, 0
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.A)no, 7
B)yes, 7
C)no, 0
D)yes, 5
E)yes, 0
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9
For the cost function, find the marginal cost at the given production level x .
A)$5.00 per item
B)$5.20 per item
C)$4.80 per item
D)$4.81 per item
E)$4.78 per item
A)$5.00 per item
B)$5.20 per item
C)$4.80 per item
D)$4.81 per item
E)$4.78 per item
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10
Evaluate the following derivative.
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11
Find the slope of the tangent to the graph of the given function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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12
Given. Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________ Unlock Deck
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13
Use the shortcut rules to calculate the derivative of the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Find the derivative of the function.
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15
Given. Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________
Say whether L Hospital s rule applies. __________ It is does, use it to evaluate the given limit. If not, use some other method. __________ Unlock Deck
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16
The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption (in milliliters per hour)can be approximated by where t is the time (in days)since the egg was laid. (An egg will typically hatch at around .)Find .
A)
B)
C)
D)
E)
where t is the time (in days)since the egg was laid. (An egg will typically hatch at around .)Find .A)
B)
C)
D)
E)
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17
Find the derivative of the function.
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18
Given. Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, -5
B)no, -12
C)yes, 12
D)yes, -5
E)no, 5
Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.A)no, -5
B)no, -12
C)yes, 12
D)yes, -5
E)no, 5
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19
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
For the cost function C ( x ), find the marginal cost at the given production level x .
A)$39.96 per item
B)$49.95 per item
C)$49.97 per item
D)$51.25 per item
E)$40.00 per item
A)$39.96 per item
B)$49.95 per item
C)$49.97 per item
D)$51.25 per item
E)$40.00 per item
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21
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
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22
The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. Government clean-air subsidies to the firm are based on the formula where q is again the reduction in emissions (in pounds per day)and S is the subsidy (in dollars). Calculate the net cost function given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost?
A)q = $2, N ( q )= $2,300
B)q = $4, N ( q )= $2,300
C)q = $2, N ( q )= $4,600
D)q = $2.5, N ( q )= $2,375
E)q = $2.5, N ( q )= $2,300
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. Government clean-air subsidies to the firm are based on the formula where q is again the reduction in emissions (in pounds per day)and S is the subsidy (in dollars). Calculate the net cost function given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost?A)q = $2, N ( q )= $2,300
B)q = $4, N ( q )= $2,300
C)q = $2, N ( q )= $4,600
D)q = $2.5, N ( q )= $2,375
E)q = $2.5, N ( q )= $2,300
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23
Your company is planning to air a number of television commercials during the ABC television network s presentation of the Academy Awards. ABC is charging your company $795,000 per 30-second spot. Additional fixed costs (development and personnel costs)amount to $400,000, and the network has agreed to provide a discount of for x television spots. Compute marginal cost and average cost .
A)
B)
C)
D)
E)
for x television spots. Compute marginal cost and average cost .A)
B)
C)
D)
E)
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24
The cost of producing x teddy bears per day at the Cuddly Companion Company is calculated by their marketing staff to be given by the formula . Evaluate the average cost .
A)$32.00
B)$29.50
C)$28.00
D)$3,249.50
E)$3,200.00
. Evaluate the average cost .A)$32.00
B)$29.50
C)$28.00
D)$3,249.50
E)$3,200.00
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25
Assume that the demand function for tuna in a small coastal town is given by where p is the price (in dollars)per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in 1 month. Calculate the price that the town s fishery should charge for tuna in order to produce a demand of 625 pounds of tuna per month.
A)$1
B)$32
C)$1,200
D)$800
E)$2
where p is the price (in dollars)per pound of tuna and q is the number of pounds of tuna that can be sold at the price p in 1 month. Calculate the price that the town s fishery should charge for tuna in order to produce a demand of 625 pounds of tuna per month.A)$1
B)$32
C)$1,200
D)$800
E)$2
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26
The cost, in thousands of dollars, of airing x television commercials during a Super Bowl game is given by the formula . Estimate how fast (in dollars per television commercial)the cost is going up when x = 8.
A)$1,500
B)$1,500,032
C)$1,500,0
D)$1,499,984
E)$1,499,968
. Estimate how fast (in dollars per television commercial)the cost is going up when x = 8.A)$1,500
B)$1,500,032
C)$1,500,0
D)$1,499,984
E)$1,499,968
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27
Your Porsche s gas mileage (in miles per gallon)is given as a function M ( x )of speed x in miles per hour. It is found that . Find M (30), M (70)and M (95).
A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049
. Find M (30), M (70)and M (95).A)M '(70)= 0.0049, M '(30)= 0, M '(95)= -0.000051
B)M '(70)= 0.0049, M '(70)= 0, M '(95)= -0.000051
C)M '(30)= 0.0049, M '(70)= 0, M '(95)= -0.000051
D)M '(30)= 0.0001, M '(70)= -0.0049, M '(95)= 0
E)M '(30)= 0.0001, M '(70)= 0, M '(95)= -0.0049
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28
Find the value of x for which the marginal profit is zero.
A)x = -5,000
B)x = 10,000
C)x = 5,000
D)x = 7,000
E)x = 2,500
A)x = -5,000
B)x = 10,000
C)x = 5,000
D)x = 7,000
E)x = 2,500
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29
The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?
A)$1,400
B)$2,800
C)$7,800
D)$2,100
E)$700
where q is the reduction in emissions (in pounds of pollutant per day)and C is the daily cost (in dollars)of this reduction. If a firm is currently reducing its emissions by 7 pounds each day, what is the marginal cost of reducing emissions even further?A)$1,400
B)$2,800
C)$7,800
D)$2,100
E)$700
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30
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
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31
Calculate .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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32
The estimated marginal revenue for sales of ESU soccer team T-shirts is given by where p is the price (in dollars)the soccer player charge for each shirt. Find R (1), R (5), R (8). Select the correct answer rounded to four decimal places.
A)R '(5)= 0.0049, R '(8)= 0, R '(1)= -3.9987
B)R '(1)= 3.9987, R '(5)= -0.0049, R '(8)= 0
C)R '(1)= -3.9987, R '(5)= 0, R '(8)= -0.0049
D)R '(1)= 0.0049, R '(5)= 0, R '(8)= -3.9987
E)R '(5)= 0.0049, R '(1)= 0, R '(8)= -3.9987
where p is the price (in dollars)the soccer player charge for each shirt. Find R (1), R (5), R (8). Select the correct answer rounded to four decimal places.A)R '(5)= 0.0049, R '(8)= 0, R '(1)= -3.9987
B)R '(1)= 3.9987, R '(5)= -0.0049, R '(8)= 0
C)R '(1)= -3.9987, R '(5)= 0, R '(8)= -0.0049
D)R '(1)= 0.0049, R '(5)= 0, R '(8)= -3.9987
E)R '(5)= 0.0049, R '(1)= 0, R '(8)= -3.9987
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33
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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34
Calculate .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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35
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
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36
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
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37
According to the equation given, a toy manufacturer calculates its daily profit P (in dollars)based on the number of workers n it employs. Calculate the marginal product at an employment level of 100 workers.
A)$39,960
B)$36,000
C)$3,999,960
D)$320
E)$440
Calculate the marginal product at an employment level of 100 workers.A)$39,960
B)$36,000
C)$3,999,960
D)$320
E)$440
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38
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
39
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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40
Your monthly profit (in dollars)from selling magazines is given by where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.
A)P (100)= $215, P '(100)= $2.08
B)P (100)= $430, P '(100)= $4.15
C)P (100)= $417.32, P '(100)= $0.35
D)P (100)= $417.32, P '(100)= $4.15
E)P (100)= $860, P '(100)= $4.65
where x is the number of magazines you sell in a month. If you are currently selling x = 100 magazines per month, find your profit and your marginal profit.A)P (100)= $215, P '(100)= $2.08
B)P (100)= $430, P '(100)= $4.15
C)P (100)= $417.32, P '(100)= $0.35
D)P (100)= $417.32, P '(100)= $4.15
E)P (100)= $860, P '(100)= $4.65
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41
The monthly sales of Sunny Electronics new stereo system is given by hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction. Please enter your answer in dollars/month without the units.
hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction. Please enter your answer in dollars/month without the units. Unlock Deck
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42
Find the equation of the line tangent to the graph of the given function at the point .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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43
The Verhulst model for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula: where p is the total population in thousands of organisms, and are constants that depend on the particular circumstances and organism being studied, and is the reproduction rate in thousands of organisms per hour. If and , find .
A)
B)
C)
D)
E)
where p is the total population in thousands of organisms, and are constants that depend on the particular circumstances and organism being studied, and is the reproduction rate in thousands of organisms per hour. If and , find .A)
B)
C)
D)
E)
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44
Find the equation of the line tangent to the graph of the given function at the point with .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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45
The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months?
A)$0.39 per month
B)$0.01 per month
C)-$0.18 per month
D)$0.29 per month
E)$0.10 per month
dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months?A)$0.39 per month
B)$0.01 per month
C)-$0.18 per month
D)$0.29 per month
E)$0.10 per month
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46
Compute the indicated derivative using the chain rule.
A)-4
B)8
C)
D)-2
E)
A)-4
B)8
C)
D)-2
E)
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47
Your Porche s gas mileage (in miles per gallon)is given as a function of speed in miles per hour. Calculate .
A)
B)
C)
D)
E)
of speed in miles per hour. Calculate .A)
B)
C)
D)
E)
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48
Calculate the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 106 flashcards in this deck.
Unlock Deck
k this deck
49
Find the indicated derivative. Please round the answer to the nearest hundredth.
A)
B)
C)
D)
E)
Please round the answer to the nearest hundredth.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
50
The Thoroughbred Bus Company finds that its monthly costs for one particular year were given by dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months? Enter your answer in dollars/month rounded to the nearest cent and without the units.
dollars after months. After months, the company had passengers per month. How fast was its cost per passenger changing after months? Enter your answer in dollars/month rounded to the nearest cent and without the units. Unlock Deck
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51
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
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52
Compute the derivative.
A)92
B)36
C)59
D)72
E)78
A)92
B)36
C)59
D)72
E)78
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53
Compute the derivative.
A)9
B)5
C)3
D)0
E)1
A)9
B)5
C)3
D)0
E)1
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54
Find the indicated derivative. Please round the answer to the nearest hundredth.
A)
B)
C)
D)
E)
Please round the answer to the nearest hundredth.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
55
The monthly sales of Sunny Electronics new stereo system is given by hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction.
A)-$473,000 per month
B)-$567,500 per month
C)$31,840 per month
D)$318,400 per month
E)$197,600 per month
hundred units per month, months after its introduction. The price Sunny charges is dollars per stereo system, months after its introduction. The revenue Sunny earns then must be . Find the rate of change of revenue months after introduction.A)-$473,000 per month
B)-$567,500 per month
C)$31,840 per month
D)$318,400 per month
E)$197,600 per month
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k this deck
56
Calculate . You need not expand your answer.
A)
B)
C)
D)
E)
. You need not expand your answer. A)
B)
C)
D)
E)
Unlock Deck
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57
Find the equation of the line tangent to the graph of the given function at the point .
. Unlock Deck
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58
Find the indicated derivative. The independent variable is a function of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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k this deck
59
Calculate the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
60
Compute the indicated derivative using the chain rule.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
Find the derivative of the function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
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k this deck
62
The soap bubble I am blowing has a radius that is growing at a rate of 9 cm/s. How fast is the surface area growing when the radius is 14 cm? (The surface area of a sphere of radius r is .)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
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k this deck
63
Find the derivative of the function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Unlock Deck
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k this deck
64
Find the derivative of the following function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
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65
The Pentagon is planning to build a new satellite that will be spherical. As is typical in these cases, the specifications keep changing, so that the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.5 foot/week. Its cost will be $1,000 per cubic foot. At the point when the plans call for a satellite 5 feet in radius, how fast is the cost growing? (The volume of a solid sphere of radius r is .)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
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66
Find the derivative of the function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
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67
Find the derivative of the function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Unlock Deck
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68
Find the derivative of the function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Unlock Deck
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69
Compute the indicated derivative using the chain rule.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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70
An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the slick is growing at a rate of 7 miles per hour, find the rate at which the area is increasing when the radius is 6 miles. (The area of a disc of radius r is .)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
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71
Match between columns
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72
Find the equation of the tangent line for at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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73
A mold culture in a dorm refrigerator is circular and growing. The radius is increasing at a rate of 0.4 cm/day. How fast is the area growing when the culture is 3 centimeters in radius? (The area of a disc of radius r is .)
A)
B)
C)
D)
E)
.)A)
B)
C)
D)
E)
Unlock Deck
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74
Calculate the derivative of the function. Please enter your answer as an expression.
Please enter your answer as an expression. Unlock Deck
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75
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
76
Calculate the derivative of the function.
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77
Find the derivative of the following function.
A)
B)
C)
D)
E)none of these
A)
B)
C)
D)
E)none of these
Unlock Deck
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78
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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79
The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 24,000 CDs per day and .
where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute at a production level of 24,000 CDs per day and . Unlock Deck
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80
The demand for the Cyberpunk II arcade video game is modeled by the logistic curve where q ( t )is the total number of units sold t months after the game s introduction. Use technology to estimate . Assume that the manufacturers of Cyberpunk II sell each unit for $600. What is the company s marginal revenue, ? Use the chain rule to estimate the rate at which revenue is growing 5 months after the introduction of the video game. Please round each answer to the nearest whole number.
A)
B)
C)
D)
E)
where q ( t )is the total number of units sold t months after the game s introduction. Use technology to estimate . Assume that the manufacturers of Cyberpunk II sell each unit for $600. What is the company s marginal revenue, ? Use the chain rule to estimate the rate at which revenue is growing 5 months after the introduction of the video game. Please round each answer to the nearest whole number.A)
B)
C)
D)
E)
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k this deck
Unlock Deck
Unlock for access to all 106 flashcards in this deck.
