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Deck 2: Differentiation
Full screen (f)
Question
Find an equation of the line that is tangent to the graph of f and parallel to the given line.
, 
A) 
B) 
C) 
D) 
E) none of the above
, A)
B)
C)
D)
E) none of the above
Question
Determine the point(s),(if any),at which the graph of the function has a horizontal tangent.
A) 0
B) 0 and 3
C) 0 and -3
D) 3
E) There are no points at which the graph has a horizontal tangent.
A) 0
B) 0 and 3
C) 0 and -3
D) 3
E) There are no points at which the graph has a horizontal tangent.
Question
Find the derivative of the function 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find an equation of the line that is tangent to the graph of f and parallel to the given line.
, 
A) 
B) 
C) 
D) 
E) both B and D
, A)
B)
C)
D)
E) both B and D
Question
Differentiate the given function.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Find the slope of the tangent line to the graph of the function below at the given point. 
, 
A) 4
B) -4
C) -2
D) 6
E) none of the above
, A) 4
B) -4
C) -2
D) 6
E) none of the above
Question
For the function given,find 
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
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Identify a function f(x)that has the given characteristics and then sketch the function. 
; 
; 
A) 
B) 
C) 
D) 
E) 
; ; A)
B)
C)
D)
E)
Question
Find the derivative of the following function using the limiting process. 
A) 
B) 
C) 
D) 
E) either B or D
A)
B)
C)
D)
E) either B or D
Question
Find the slope of the tangent line to the graph of the function below at the given point. 
, 
A) -12
B) -2
C) 10
D) -18
E) none of the above
, A) -12
B) -2
C) 10
D) -18
E) none of the above
Question
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Find the slope of the tangent line to the graph of the function below at the given point. 
, 
A) 12
B) -3
C) -8
D) -12
E) none of the above
, A) 12
B) -3
C) -8
D) -12
E) none of the above
Question
Find the derivative of the following function using the limiting process. 
A) 2
B) 
C) 
D) 
E) none of the above
A) 2
B)
C)
D)
E) none of the above
Question
Differentiate the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the derivative of the following function using the limiting process.
A) 
B) 
C) 
D) 
E) none of the above
A)
B)
C)
D)
E) none of the above
Question
Use the limit definition to find the slope of the tangent line to the graph of 
at the point 
A) 
B) 
C) 
D) 
E) 
at the point A)
B)
C)
D)
E)
Question
The graph shows the number of visitors V to a national park in hundreds of thousands during a one-year period,where 
represents January.Estimate the rate of change of V over the interval 
Round your answer to the nearest hundred thousand visitors per year. 
A) 187.5 hundred thousand visitors per year
B) 281.25 hundred thousand visitors per year
C) 225 hundred thousand visitors per year
D) 562.5 hundred thousand visitors per year
E) 1125 hundred thousand visitors per year
represents January.Estimate the rate of change of V over the interval Round your answer to the nearest hundred thousand visitors per year. A) 187.5 hundred thousand visitors per year
B) 281.25 hundred thousand visitors per year
C) 225 hundred thousand visitors per year
D) 562.5 hundred thousand visitors per year
E) 1125 hundred thousand visitors per year
Question
The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by 
where t is the year,with 
corresponding to 1980.Determine the population growth rate, 
A) 
B) 
C) 
D) 
E) 
where t is the year,with corresponding to 1980.Determine the population growth rate, A)
B)
C)
D)
E)
Question
The cost C (in dollars)of producing x units of a product is given by 
Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places.
A) $0.58
B) $0.36
C) $0.62
D) $0.12
E) $0.64
Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. A) $0.58
B) $0.36
C) $0.62
D) $0.12
E) $0.64
Question
A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by 
where t is the time (in hours).Find the rate of change of the population when 
A) 21.95 bacteria/hr
B) 3.53 bacteria/hr
C) 10.6 bacteria/hr
D) 2.07 bacteria/hr
E) 7.32 bacteria/hr
where t is the time (in hours).Find the rate of change of the population when A) 21.95 bacteria/hr
B) 3.53 bacteria/hr
C) 10.6 bacteria/hr
D) 2.07 bacteria/hr
E) 7.32 bacteria/hr
Question
Find the point(s),if any,at which the graph of f has a horizontal tangent line. 
A) 
, 
B) 
, 
C) 
, 
D) 
, 
E) 
, 
A)
, B)
, C)
, D)
, E)
, Question
Use the demand function 
to find the rate of change in the demand x for the given price 
Round your answer to two decimal places.
A) 1.44 units per dollar
B) -0.72 units per dollar
C) 0.72 units per dollar
D) 0.96 units per dollar
E) -1.44 units per dollar
to find the rate of change in the demand x for the given price Round your answer to two decimal places. A) 1.44 units per dollar
B) -0.72 units per dollar
C) 0.72 units per dollar
D) 0.96 units per dollar
E) -1.44 units per dollar
Question
The profit (in dollars)from selling x units of calculus textbooks is given by 
Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.
A) $15.35
B) $30.00
C) $15.45
D) $30.80
E) $30.60
Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. A) $15.35
B) $30.00
C) $15.45
D) $30.80
E) $30.60
Question
Use the product Rule to find the derivative of the function 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of f at the given point. 
,at 
A) 
B) 
C) 
D) 
E) 
,at A)
B)
C)
D)
E)
Question
The profit (in dollars)from selling x units of calculus textbooks is given by 
Find the marginal profit when 
Round your answer to two decimal places.
A) $35.00
B) $20.00
C) $5.00
D) $-125.00
E) $-130.05
Find the marginal profit when Round your answer to two decimal places. A) $35.00
B) $20.00
C) $5.00
D) $-125.00
E) $-130.05
Question
Find an equation of the tangent line to the graph of f at the given point. 
,at 
A) 
B) 
C) 
D) 
E) 
,at A)
B)
C)
D)
E)
Question
When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $25,respectively.Find the profit P as a function of x,the number of glasses of lemonade sold.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by 
where t is the time (in hours).Find the rate of change of the population when 
A) 36.98 bacteria/hr
B) 29.15 bacteria/hr
C) 33.65 bacteria/hr
D) 32.75 bacteria/hr
E) 30.25 bacteria/hr
where t is the time (in hours).Find the rate of change of the population when A) 36.98 bacteria/hr
B) 29.15 bacteria/hr
C) 33.65 bacteria/hr
D) 32.75 bacteria/hr
E) 30.25 bacteria/hr
Question
Find the derivative of the function 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use the given information to find 
of the function 
, 
, 
and 
A) 
B) 
C) 
D) 
E) 
of the function , , and A)
B)
C)
D)
E)
Question
Find the derivative of the function 
State which differentiation rule(s)you used to find the derivative.
A) 1, Product Rule.
B) 1, Quotient Rule.
C) 5, Product Rule.
D) 5, Quotient Rule.
E) 
,Product Rule.
State which differentiation rule(s)you used to find the derivative. A) 1, Product Rule.
B) 1, Quotient Rule.
C) 5, Product Rule.
D) 5, Quotient Rule.
E)
,Product Rule. Question
Find the marginal cost for producing x units.(The cost is measured in dollars.) 
A) $9,800
B) $9,850
C) $8,800
D) $8,850
E) $9,750
A) $9,800
B) $9,850
C) $8,800
D) $8,850
E) $9,750
Question
Find the marginal revenue for producing x units.(The revenue is measured in dollars.) 
A) 
dollars
B) 
dollars
C) 50 dollars
D) 
dollars
E) 
dollars
A)
dollarsB)
dollarsC) 50 dollars
D)
dollarsE)
dollars Question
When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold.
A) 
, 
B) 
, 
C) 
, 
D) 
, 
E) 
, 
A)
, B)
, C)
, D)
, E)
, Question
Find the marginal profit for producing x units.(The profit is measured in dollars.) 
A) 
dollars
B)
dollars
C) 
dollars
D) 
dollars
E) 
dollars
A)
dollarsB)
dollarsC)
dollarsD)
dollarsE)
dollars Question
Find the second derivative of the function. 
A) 
B) 
C) 
D) 
E) None of the above
A)
B)
C)
D)
E) None of the above
Question
Find the indicated derivative.
Find
if 
A) 
B) 
C) 
D) 
E) 
Find
if A)
B)
C)
D)
E)
Question
Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
If
,then 
If
,then Question
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find 
of 
, 
A)
B)
C)
D)
E) none of these choices
of , A)
B)
C)
D)
E) none of these choices
Question
You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is 
Find the rate of change of A with respect to r when 
Round your answer to two decimal places.
A) $1,375.67
B) $65,594.67
C) $114.64
D) $5,466.22
E) $5,430.02
Find the rate of change of A with respect to r when Round your answer to two decimal places. A) $1,375.67
B) $65,594.67
C) $114.64
D) $5,466.22
E) $5,430.02
Question
Find the derivative of the function.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the second derivative for the function 
and solve the equation 
A) 0
B) 4
C) -4
D) 
E) no solution
and solve the equation A) 0
B) 4
C) -4
D)
E) no solution
Question
Find the derivative of the function. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the third derivative. 
A)
B)
C) 0
D)
E)
A)
B)
C) 0
D)
E)
Question
Find the value 
for the function 
A) 20,916
B) 37,191
C) 53,170
D) 37,196
E) 184,779
for the function A) 20,916
B) 37,191
C) 53,170
D) 37,196
E) 184,779
Question
Find the second derivative for the function 
and solve the equation 
A) -2
B) 1
C) 0
D) 26
E) 33
and solve the equation A) -2
B) 1
C) 0
D) 26
E) 33
Question
Find the derivative of the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
, 
,and 
of the functions 
, 
A) 
, 
, and 
B) 
, 
, and 
C) 
, 
, and 
D) 
, 
, and 
E) 
, 
,and 
, ,and of the functions , A)
, , and B)
, , and C)
, , and D)
, , and E)
, ,and Question
Find the 
of 
A) 
B) 
C) 
D) 
E) 
of A)
B)
C)
D)
E)
Question
Find the third derivative of the function 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time.
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
Differentiate the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The value V of a machine t years after it is purchased is inversely proportional to the square root of 
The initial value of the machine is $10,000.Find the rate of depreciation when 
Round your answer to two decimal places.
A) -381.80 per year
B) -1,889.82 per year
C) 447.21 per year
D) 1,767.77 per year
E) -763.60 per year
The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places. A) -381.80 per year
B) -1,889.82 per year
C) 447.21 per year
D) 1,767.77 per year
E) -763.60 per year
Question
Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the slope of the graph at the given point. 
A) 0
B) 3
C) 5
D) 4
E) 7
A) 0
B) 3
C) 5
D) 4
E) 7
Question
Find 
for the equation 
by implicit differentiation and evaluate the derivative at the point 
A)
B)
C)
D)
E) 0
for the equation by implicit differentiation and evaluate the derivative at the point A)
B)
C)
D)
E) 0
Question
Assume that x and y are differentiable functions of t.Find 
using the given values. 
for 
, 
A) 216
B) 82
C) 164
D) 214
E) 107
using the given values. for , A) 216
B) 82
C) 164
D) 214
E) 107
Question
Find 
implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating 
at the point. 
A) 
B) 
C) 
D) 
E) 
implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point. A)
B)
C)
D)
E)
Question
Question
A point is moving along the graph of the function 
such that 
centimeters per second. Find 
when 
A) 
B) 
C) 
D) 
E) 
such that centimeters per second. Find when A)
B)
C)
D)
E)
Question
A point is moving along the graph of the function 
such that 
centimeters per second. Find 
for the given values of x.
A) 
B) 
C) 
D) 
E) 
such that centimeters per second. Find for the given values of x.
A)
B)
C)
D)
E)
Question
Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the slope of the graph at the given point. 
A) 2
B) 0
C) 1
D) 3
E) 5
A) 2
B) 0
C) 1
D) 3
E) 5
Question
Assume that x and y are differentiable functions of t.Find 
given that 
, 
,and 
A) -1.33
B) 1.5
C) 6
D) -8
E) 2.67
given that , ,and A) -1.33
B) 1.5
C) 6
D) -8
E) 2.67
Question
Assume that x and y are differentiable functions of t.Given 
,find 
when 
and 
A) 
B) 
C) 
D) 
E) 
,find when and A)
B)
C)
D)
E)
Question
Find the rate of change of x with respect to p. 
, 
A) 
B) 
C) 
D) 
E) 
, A)
B)
C)
D)
E)
Question
The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when 
inches.Round your answer to one decimal place.
A) 1,809.6 cubic inches per minute
B) 7,238.2 cubic inches per minute
C) 36,191.1 cubic inches per minute
D) 9,047.8 cubic inches per minute
E) 27,143.4 cubic inches per minute
inches.Round your answer to one decimal place. A) 1,809.6 cubic inches per minute
B) 7,238.2 cubic inches per minute
C) 36,191.1 cubic inches per minute
D) 9,047.8 cubic inches per minute
E) 27,143.4 cubic inches per minute
Question
Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by 
Find the rate of change of y with respect to x when 
and 
A) -2
B) 0
C) 3
D) -7
E) 5
Find the rate of change of y with respect to x when and A) -2
B) 0
C) 3
D) -7
E) 5
Question
Find 
for the following equation: 
A) 
B) 
C) 
D) 
E) 
for the following equation: A)
B)
C)
D)
E)
Question
Find the rate of change of x with respect to p. 
, 
A) 
B) 
C) 
D) 
E) 
, A)
B)
C)
D)
E)
Question
Find 
for the equation 
A) 
B) 
C) 
D) 
E) 
for the equation A)
B)
C)
D)
E)
Question
Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are 
and 
At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month?
A) 11,960 per month
B) 1,160 per month
C) 1,960 per month
D) 760 per month
E) 19,960 per month
and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? A) 11,960 per month
B) 1,160 per month
C) 1,960 per month
D) 760 per month
E) 19,960 per month
Question
Find 
implicitly for 
A) 
B) 
C) 
D) 
E) 
implicitly for A)
B)
C)
D)
E)
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Full screen (f)
Deck 2: Differentiation
1
Find an equation of the line that is tangent to the graph of f and parallel to the given line.
,
A)
B)
C)
D)
E) none of the above
, A)
B)
C)
D)
E) none of the above
2
Determine the point(s),(if any),at which the graph of the function has a horizontal tangent.
A) 0
B) 0 and 3
C) 0 and -3
D) 3
E) There are no points at which the graph has a horizontal tangent.
A) 0
B) 0 and 3
C) 0 and -3
D) 3
E) There are no points at which the graph has a horizontal tangent.
3
3
Find the derivative of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find an equation of the line that is tangent to the graph of f and parallel to the given line.
,
A)
B)
C)
D)
E) both B and D
, A)
B)
C)
D)
E) both B and D
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Unlock for access to all 84 flashcards in this deck.
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5
Differentiate the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Find the derivative of the function.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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7
Find the derivative of the function.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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Unlock for access to all 84 flashcards in this deck.
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8
Find the slope of the tangent line to the graph of the function below at the given point. ,
A) 4
B) -4
C) -2
D) 6
E) none of the above
, A) 4
B) -4
C) -2
D) 6
E) none of the above
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9
For the function given,find
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Find the derivative of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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11
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 84 flashcards in this deck.
Unlock Deck
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12
Identify a function f(x)that has the given characteristics and then sketch the function. ; ;
A)
B)
C)
D)
E)
; ; A)
B)
C)
D)
E)
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13
Find the derivative of the following function using the limiting process.
A)
B)
C)
D)
E) either B or D
A)
B)
C)
D)
E) either B or D
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k this deck
14
Find the slope of the tangent line to the graph of the function below at the given point. ,
A) -12
B) -2
C) 10
D) -18
E) none of the above
, A) -12
B) -2
C) 10
D) -18
E) none of the above
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15
Find the derivative of the function.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
16
Find the slope of the tangent line to the graph of the function below at the given point. ,
A) 12
B) -3
C) -8
D) -12
E) none of the above
, A) 12
B) -3
C) -8
D) -12
E) none of the above
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Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
17
Find the derivative of the following function using the limiting process.
A) 2
B)
C)
D)
E) none of the above
A) 2
B)
C)
D)
E) none of the above
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k this deck
18
Differentiate the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
19
Find the derivative of the following function using the limiting process.
A)
B)
C)
D)
E) none of the above
A)
B)
C)
D)
E) none of the above
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k this deck
20
Use the limit definition to find the slope of the tangent line to the graph of at the point
A)
B)
C)
D)
E)
at the point A)
B)
C)
D)
E)
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k this deck
21
The graph shows the number of visitors V to a national park in hundreds of thousands during a one-year period,where represents January.Estimate the rate of change of V over the interval Round your answer to the nearest hundred thousand visitors per year.
A) 187.5 hundred thousand visitors per year
B) 281.25 hundred thousand visitors per year
C) 225 hundred thousand visitors per year
D) 562.5 hundred thousand visitors per year
E) 1125 hundred thousand visitors per year
represents January.Estimate the rate of change of V over the interval Round your answer to the nearest hundred thousand visitors per year. A) 187.5 hundred thousand visitors per year
B) 281.25 hundred thousand visitors per year
C) 225 hundred thousand visitors per year
D) 562.5 hundred thousand visitors per year
E) 1125 hundred thousand visitors per year
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22
The population P ( in thousands)of Japan from 1980 through 2010 can be modeled by where t is the year,with corresponding to 1980.Determine the population growth rate,
A)
B)
C)
D)
E)
where t is the year,with corresponding to 1980.Determine the population growth rate, A)
B)
C)
D)
E)
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k this deck
23
The cost C (in dollars)of producing x units of a product is given by Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places.
A) $0.58
B) $0.36
C) $0.62
D) $0.12
E) $0.64
Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. A) $0.58
B) $0.36
C) $0.62
D) $0.12
E) $0.64
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k this deck
24
A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when
A) 21.95 bacteria/hr
B) 3.53 bacteria/hr
C) 10.6 bacteria/hr
D) 2.07 bacteria/hr
E) 7.32 bacteria/hr
where t is the time (in hours).Find the rate of change of the population when A) 21.95 bacteria/hr
B) 3.53 bacteria/hr
C) 10.6 bacteria/hr
D) 2.07 bacteria/hr
E) 7.32 bacteria/hr
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k this deck
25
Find the point(s),if any,at which the graph of f has a horizontal tangent line.
A) ,
B) ,
C) ,
D) ,
E) ,
A)
, B)
, C)
, D)
, E)
, Unlock Deck
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26
Use the demand function to find the rate of change in the demand x for the given price Round your answer to two decimal places.
A) 1.44 units per dollar
B) -0.72 units per dollar
C) 0.72 units per dollar
D) 0.96 units per dollar
E) -1.44 units per dollar
to find the rate of change in the demand x for the given price Round your answer to two decimal places. A) 1.44 units per dollar
B) -0.72 units per dollar
C) 0.72 units per dollar
D) 0.96 units per dollar
E) -1.44 units per dollar
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27
The profit (in dollars)from selling x units of calculus textbooks is given by Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places.
A) $15.35
B) $30.00
C) $15.45
D) $30.80
E) $30.60
Find the additional profit when the sales increase from 146 to 147 units.Round your answer to two decimal places. A) $15.35
B) $30.00
C) $15.45
D) $30.80
E) $30.60
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k this deck
28
Use the product Rule to find the derivative of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
29
Find an equation of the tangent line to the graph of f at the given point. ,at
A)
B)
C)
D)
E)
,at A)
B)
C)
D)
E)
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k this deck
30
The profit (in dollars)from selling x units of calculus textbooks is given by Find the marginal profit when Round your answer to two decimal places.
A) $35.00
B) $20.00
C) $5.00
D) $-125.00
E) $-130.05
Find the marginal profit when Round your answer to two decimal places. A) $35.00
B) $20.00
C) $5.00
D) $-125.00
E) $-130.05
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k this deck
31
Find an equation of the tangent line to the graph of f at the given point. ,at
A)
B)
C)
D)
E)
,at A)
B)
C)
D)
E)
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k this deck
32
When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $25,respectively.Find the profit P as a function of x,the number of glasses of lemonade sold.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
33
A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when
A) 36.98 bacteria/hr
B) 29.15 bacteria/hr
C) 33.65 bacteria/hr
D) 32.75 bacteria/hr
E) 30.25 bacteria/hr
where t is the time (in hours).Find the rate of change of the population when A) 36.98 bacteria/hr
B) 29.15 bacteria/hr
C) 33.65 bacteria/hr
D) 32.75 bacteria/hr
E) 30.25 bacteria/hr
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k this deck
34
Find the derivative of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
k this deck
35
Use the given information to find of the function , , and
A)
B)
C)
D)
E)
of the function , , and A)
B)
C)
D)
E)
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k this deck
36
Find the derivative of the function State which differentiation rule(s)you used to find the derivative.
A) 1, Product Rule.
B) 1, Quotient Rule.
C) 5, Product Rule.
D) 5, Quotient Rule.
E) ,Product Rule.
State which differentiation rule(s)you used to find the derivative. A) 1, Product Rule.
B) 1, Quotient Rule.
C) 5, Product Rule.
D) 5, Quotient Rule.
E)
,Product Rule. Unlock Deck
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37
Find the marginal cost for producing x units.(The cost is measured in dollars.)
A) $9,800
B) $9,850
C) $8,800
D) $8,850
E) $9,750
A) $9,800
B) $9,850
C) $8,800
D) $8,850
E) $9,750
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38
Find the marginal revenue for producing x units.(The revenue is measured in dollars.)
A) dollars
B) dollars
C) 50 dollars
D) dollars
E) dollars
A)
dollarsB)
dollarsC) 50 dollars
D)
dollarsE)
dollars Unlock Deck
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Unlock Deck
k this deck
39
When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold.
A) ,
B) ,
C) ,
D) ,
E) ,
A)
, B)
, C)
, D)
, E)
, Unlock Deck
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k this deck
40
Find the marginal profit for producing x units.(The profit is measured in dollars.)
A) dollars
B) dollars
C) dollars
D) dollars
E) dollars
A)
dollarsB)
dollarsC)
dollarsD)
dollarsE)
dollars Unlock Deck
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Unlock Deck
k this deck
41
Find the second derivative of the function.
A)
B)
C)
D)
E) None of the above
A)
B)
C)
D)
E) None of the above
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k this deck
42
Find the indicated derivative.
Find if
A)
B)
C)
D)
E)
Find
if A)
B)
C)
D)
E)
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k this deck
43
Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
If ,then
If
,then Unlock Deck
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44
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
45
Find of ,
A)
B)
C)
D)
E) none of these choices
of , A)
B)
C)
D)
E) none of these choices
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k this deck
46
You deposit $1,000 in an account with an annual interest rate of change r (in decimal form)compounded monthly.At the end of 4 years,the balance is Find the rate of change of A with respect to r when Round your answer to two decimal places.
A) $1,375.67
B) $65,594.67
C) $114.64
D) $5,466.22
E) $5,430.02
Find the rate of change of A with respect to r when Round your answer to two decimal places. A) $1,375.67
B) $65,594.67
C) $114.64
D) $5,466.22
E) $5,430.02
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k this deck
47
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
48
Find the second derivative for the function and solve the equation
A) 0
B) 4
C) -4
D)
E) no solution
and solve the equation A) 0
B) 4
C) -4
D)
E) no solution
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k this deck
49
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
50
Find the third derivative.
A)
B)
C) 0
D)
E)
A)
B)
C) 0
D)
E)
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Unlock Deck
k this deck
51
Find the value for the function
A) 20,916
B) 37,191
C) 53,170
D) 37,196
E) 184,779
for the function A) 20,916
B) 37,191
C) 53,170
D) 37,196
E) 184,779
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Unlock Deck
k this deck
52
Find the second derivative for the function and solve the equation
A) -2
B) 1
C) 0
D) 26
E) 33
and solve the equation A) -2
B) 1
C) 0
D) 26
E) 33
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k this deck
53
Find the derivative of the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
54
Find , ,and of the functions ,
A) , , and
B) , , and
C) , , and
D) , , and
E) , ,and
, ,and of the functions , A)
, , and B)
, , and C)
, , and D)
, , and E)
, ,and Unlock Deck
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55
Find the of
A)
B)
C)
D)
E)
of A)
B)
C)
D)
E)
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Unlock Deck
k this deck
56
Find the third derivative of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
57
A brick becomes dislodged from the Empire State Building (at a height of 1,000 feet)and falls to the sidewalk below.Write the position s(t),velocity v(t),and acceleration a(t)as functions of time.
A) ; ;
B) ; ;
C) ; ;
D) ; ;
E) ; ;
A)
; ; B)
; ; C)
; ; D)
; ; E)
; ; Unlock Deck
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58
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 84 flashcards in this deck.
Unlock Deck
k this deck
59
Differentiate the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
k this deck
60
The value V of a machine t years after it is purchased is inversely proportional to the square root of The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places.
A) -381.80 per year
B) -1,889.82 per year
C) 447.21 per year
D) 1,767.77 per year
E) -763.60 per year
The initial value of the machine is $10,000.Find the rate of depreciation when Round your answer to two decimal places. A) -381.80 per year
B) -1,889.82 per year
C) 447.21 per year
D) 1,767.77 per year
E) -763.60 per year
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61
Area.The radius,r,of a circle is decreasing at a rate of 4 centimeters per minute. Find the rate of change of area,A,when the radius is 6.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
62
Find the slope of the graph at the given point.
A) 0
B) 3
C) 5
D) 4
E) 7
A) 0
B) 3
C) 5
D) 4
E) 7
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k this deck
63
Find for the equation by implicit differentiation and evaluate the derivative at the point
A)
B)
C)
D)
E) 0
for the equation by implicit differentiation and evaluate the derivative at the point A)
B)
C)
D)
E) 0
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k this deck
64
Assume that x and y are differentiable functions of t.Find using the given values. for ,
A) 216
B) 82
C) 164
D) 214
E) 107
using the given values. for , A) 216
B) 82
C) 164
D) 214
E) 107
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Unlock Deck
k this deck
65
Find implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point.
A)
B)
C)
D)
E)
implicitly and explicitly(the explicit functions are shown on the graph)and show that the results are equivalent.Use the graph to estimate the slope of the tangent line at the labeled point.Then verify your result analytically by evaluating at the point. A)
B)
C)
D)
E)
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k this deck
66
The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?
A) 96 ft2/min
B) 1,008 ft2/min
C) 504 ft2/min
D) 2,016 ft2/min
E) 84 ft2/min
A) 96 ft2/min
B) 1,008 ft2/min
C) 504 ft2/min
D) 2,016 ft2/min
E) 84 ft2/min
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k this deck
67
A point is moving along the graph of the function such that centimeters per second. Find when
A)
B)
C)
D)
E)
such that centimeters per second. Find when A)
B)
C)
D)
E)
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k this deck
68
A point is moving along the graph of the function such that centimeters per second. Find for the given values of x.
A)
B)
C)
D)
E)
such that centimeters per second. Find for the given values of x.
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
69
Volume and radius.Suppose that air is being pumped into a spherical balloon at a rate of 8 in.3/min.At what rate is the radius of the balloon increasing when the radius is 7 in.?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
70
Find the slope of the graph at the given point.
A) 2
B) 0
C) 1
D) 3
E) 5
A) 2
B) 0
C) 1
D) 3
E) 5
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k this deck
71
Assume that x and y are differentiable functions of t.Find given that , ,and
A) -1.33
B) 1.5
C) 6
D) -8
E) 2.67
given that , ,and A) -1.33
B) 1.5
C) 6
D) -8
E) 2.67
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k this deck
72
Assume that x and y are differentiable functions of t.Given ,find when and
A)
B)
C)
D)
E)
,find when and A)
B)
C)
D)
E)
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k this deck
73
Find the rate of change of x with respect to p. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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k this deck
74
The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when inches.Round your answer to one decimal place.
A) 1,809.6 cubic inches per minute
B) 7,238.2 cubic inches per minute
C) 36,191.1 cubic inches per minute
D) 9,047.8 cubic inches per minute
E) 27,143.4 cubic inches per minute
inches.Round your answer to one decimal place. A) 1,809.6 cubic inches per minute
B) 7,238.2 cubic inches per minute
C) 36,191.1 cubic inches per minute
D) 9,047.8 cubic inches per minute
E) 27,143.4 cubic inches per minute
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k this deck
75
Let x represent the units of labor and y the capital invested in a manufacturing process.When 135,540 units are produced,the relationship between labor and capital can be modeled by Find the rate of change of y with respect to x when and
A) -2
B) 0
C) 3
D) -7
E) 5
Find the rate of change of y with respect to x when and A) -2
B) 0
C) 3
D) -7
E) 5
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k this deck
76
Find for the following equation:
A)
B)
C)
D)
E)
for the following equation: A)
B)
C)
D)
E)
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k this deck
77
Find the rate of change of x with respect to p. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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k this deck
78
Find for the equation
A)
B)
C)
D)
E)
for the equation A)
B)
C)
D)
E)
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k this deck
79
Profit.Suppose that the monthly revenue and cost (in dollars)for x units of a product are and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month?
A) 11,960 per month
B) 1,160 per month
C) 1,960 per month
D) 760 per month
E) 19,960 per month
and At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? A) 11,960 per month
B) 1,160 per month
C) 1,960 per month
D) 760 per month
E) 19,960 per month
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k this deck
80
Find implicitly for
A)
B)
C)
D)
E)
implicitly for A)
B)
C)
D)
E)
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Unlock Deck
Unlock for access to all 84 flashcards in this deck.
