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Deck 5: Differentiation
Full screen (f)
Question
Describe the x-values at which the graph of the function 
given below is differentiable. 
A)
is differentiable on the interval 
.
B)
is differentiable on the interval 
.
C)
is differentiable everywhere except at 
.
D)
is differentiable everywhere except at 
.
E)
is differentiable at 
.
given below is differentiable. A)
is differentiable on the interval .B)
is differentiable on the interval .C)
is differentiable everywhere except at .D)
is differentiable everywhere except at .E)
is differentiable at .
Question
Find the derivative of the function 
using the limiting process.
A)
B)
C)
D)
E)
using the limiting process.A)
B)
C)
D)
E)
Question
Find an equation of the a line that is tangent to the graph of f and parallel to the given line. 
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 
by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
Question
Find the derivative of the following function 
using the limiting process.
A)
B)
C)
D)
E)
using the limiting process.A)
B)
C)
D)
E)
Question
Find an equation of the line that is tangent to the graph of the function 
and parallel to the line 
.
A)
B)
C)
D)
E)
and parallel to the line .A)
B)
C)
D)
E)
Question
Find the derivative of the function 
by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
Question
Find the slope m of the line tangent to the graph of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Find the derivative of the following function using the limiting process. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use the alternative form of the derivative to find the derivative of the function 
at 
.
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
Question
Find an equation of the line that is tangent to the graph of the function 
and parallel to the line 
.
A)
B)
C)
D)
E)
and parallel to the line .A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
The graph of the function f is given below. Select the graph of 
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)
A)
B)
C)
D)
E)
Question
Find the slope m of the line tangent to the graph of the function 
at the point 
.
A)
B)
C)
D)
E)
at the 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 the derivative of the function 
by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
Question
Find an equation of the tangent line to the graph of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Use the alternative form of the derivative to find the derivative of the function 
at 
.
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
Question
A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The position function is 
.What is its velocity after 4 seconds?
A)The velocity after 4 seconds is 128.4 meters per second.
B)The velocity after 4 seconds is -167.6 meters per second.
C)The velocity after 4 seconds is -187.2 meters per second.
D)The velocity after 4 seconds is 108.8 meters per second.
E)The velocity after 4 seconds is 276.4 meters per second.
.What is its velocity after 4 seconds?A)The velocity after 4 seconds is 128.4 meters per second.
B)The velocity after 4 seconds is -167.6 meters per second.
C)The velocity after 4 seconds is -187.2 meters per second.
D)The velocity after 4 seconds is 108.8 meters per second.
E)The velocity after 4 seconds is 276.4 meters per second.
Question
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the slope of the graph of the function at the given value. 
when 
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1364 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A)2.308 sec
B)8.957 sec
C)2.172 sec
D)8.711 sec
E)9.233 sec
. A silver coin is dropped from the top of a building that is 1364 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.A)2.308 sec
B)8.957 sec
C)2.172 sec
D)8.711 sec
E)9.233 sec
Question
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
and 
C)
and 
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval 
.
A)-70 ft/sec
B)98 ft/sec
C)-98 ft/sec
D)70 ft/sec
E)-107 ft/sec
. A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval .A)-70 ft/sec
B)98 ft/sec
C)-98 ft/sec
D)70 ft/sec
E)-107 ft/sec
Question
Suppose the position function for a free-falling object on a certain planet is given by is given by 
. A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.
A)
B)
C)
D)
E)
. A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.A)
B)
C)
D)
E)
Question
Use the Quotient Rule to differentiate the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Use the Product Rule to differentiate 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
and 
C)
and 
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
Question
A ball is thrown straight down from the top of a 250-ft building with an initial velocity of -12 ft per second. The position function is 
. What is the velocity of the ball after 4 seconds?
A)The velocity after 4 seconds is -280 ft per second.
B)The velocity after 4 seconds is -116 ft per second.
C)The velocity after 4 seconds is -140 ft per second.
D)The velocity after 4 seconds is -52 ft per second..
E)The velocity after 4 seconds is -76 ft per second.
. What is the velocity of the ball after 4 seconds?A)The velocity after 4 seconds is -280 ft per second.
B)The velocity after 4 seconds is -116 ft per second.
C)The velocity after 4 seconds is -140 ft per second.
D)The velocity after 4 seconds is -52 ft per second..
E)The velocity after 4 seconds is -76 ft per second.
Question
Find the derivative of the algebraic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
The length of a rectangle is 
and its height is 
, where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.
A)
square inches/second
B)
square inches/second
C)
square inches/second
D)
square inches/second
E)
square inches/second
and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.A)
square inches/secondB)
square inches/secondC)
square inches/secondD)
square inches/secondE)
square inches/second Question
Find the derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A)-128.406 ft/sec
B)-256.811 ft/sec
C)-111.203 ft/sec
D)-267.298 ft/sec
E)-244.811 ft/sec
. A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.A)-128.406 ft/sec
B)-256.811 ft/sec
C)-111.203 ft/sec
D)-267.298 ft/sec
E)-244.811 ft/sec
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
Suppose the position function for a free-falling object on a certain planet is given by 
. A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when 
.
A)-15 ft/sec
B)-45 ft/sec
C)-29 ft/sec
D)-30 ft/sec
E)-44 ft/sec
. A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when .A)-15 ft/sec
B)-45 ft/sec
C)-29 ft/sec
D)-30 ft/sec
E)-44 ft/sec
Question
Use the rules of differentiation to 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
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
A)
B)
and 
C)
and 
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
Question
Find dy/dx by implicit differentiation. 
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
A population of 420 bacteria is introduced into a culture and grows in number according to the equation 
where t is measured in hours. Find the rate at which the population is growing when t = 5. Round your answer to two decimal places.
A)25.72 bacteria per hour
B)23.01 bacteria per hour
C)31.70 bacteria per hour
D)52.65 bacteria per hour
E)7.25 bacteria per hour
where t is measured in hours. Find the rate at which the population is growing when t = 5. Round your answer to two decimal places.A)25.72 bacteria per hour
B)23.01 bacteria per hour
C)31.70 bacteria per hour
D)52.65 bacteria per hour
E)7.25 bacteria per hour
Question
Evaluate 
for the equation 
at the given point 
Round your answer to two decimal places.
A)
B)
C)
D)
E)
for the equation at the given point Round your answer to two decimal places.A)
B)
C)
D)
E)
Question
Find the second derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Find the second 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
Find dy/dx by implicit differentiation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the second derivative of the function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the derivative of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Find the derivative of the algebraic function 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Evaluate the derivative of the function 
at the point 
.
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Suppose that an automobile's velocity starting from rest is 
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.
A)7.4 ft/sec2
B)0.4 ft/sec2
C)1.7 ft/sec2
D)0.8 ft/sec2
E)0.2 ft/sec2
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.A)7.4 ft/sec2
B)0.4 ft/sec2
C)1.7 ft/sec2
D)0.8 ft/sec2
E)0.2 ft/sec2
Question
Find the derivative of the function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate 
for the equation 
at the given point 
Round your answer to two decimal places.
A)
B)
C)
D)
E)
for the equation at the given point Round your answer to two decimal places.A)
B)
C)
D)
E)
Question
Find dy/dx by implicit differentiation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Given the derivative below find the requested higher-order derivative. 
, 
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 derivative of the function at the given point. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
Question
Assume that x and y are both differentiable functions of t . Find 
for the equation 
A)
B)
C)
D)
E)
for the equation A)
B)
C)
D)
E)
Question
Find d2y/dx2 in terms of x and y. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A spherical balloon is inflated with gas at the rate of 200 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 60 centimeters?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the points at which the graph of the equation has a vertical or horizontal tangent line. 
A)There is a horizontal tangent at
but no vertical tangents.
B)There is a horizontal tangent at
and a vertical tangent at 
.
C)There is a vertical tangent at
but no horizontal tangents.
D)There is a horizontal tangent at
and a vertical tangent at 
.
E)There are no horizontal or vertical tangent lines.
A)There is a horizontal tangent at
but no vertical tangents.B)There is a horizontal tangent at
and a vertical tangent at .C)There is a vertical tangent at
but no horizontal tangents.D)There is a horizontal tangent at
and a vertical tangent at .E)There are no horizontal or vertical tangent lines.
Question
The radius, r, of a circle is increasing at a rate of 2 centimeters per minute.Find the rate of change of area, A, when the radius is 
.
A)
sq cm/min
B)
sq cm/min
C)
sq cm/min
D)
sq cm/min
E)
sq cm/min
.A)
sq cm/minB)
sq cm/minC)
sq cm/minD)
sq cm/minE)
sq cm/min Question
A conical tank (with vertex down) is 20 feet across the top and 26 feet deep. If water is flowing into the tank at a rate of 16 cubic feet per minute, find the rate of change of the depth of the water when the water is 12 feet deep.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
in terms of x and y given that 
A)
B)
C)
D)
E)
in terms of x and y given that A)
B)
C)
D)
E)
Question
Assume that x and y are both differentiable functions of t. Find 
for the equation 
A)
B)
C)
D)
E)
for the equation A)
B)
C)
D)
E)
Question
A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is 8 feet from the wall. Round your answer to two decimal places. 
A)
ft2/sec
B)
ft2/sec
C)
ft2/sec
D)
ft2/sec
E)
ft2/sec
A)
ft2/secB)
ft2/secC)
ft2/secD)
ft2/secE)
ft2/sec Question
A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 8 feet from the base of the light, at what rate is the tip of his shadow moving? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. How fast is the top of the ladder moving down the wall when its base is 14 feet from the wall? Round your answer to two decimal places. 
A)6.86 ft/sec
B)-6.00 ft/sec
C)-3.92 ft/sec
D)8.00 ft/sec
E)-6.86 ft/sec
A)6.86 ft/sec
B)-6.00 ft/sec
C)-3.92 ft/sec
D)8.00 ft/sec
E)-6.86 ft/sec
Question
A point is moving along the graph of the function 
such that dx/dt = 5 centimeters per second.Find dy/dt when 
.
A)
B)
C)
D)
E)
such that dx/dt = 5 centimeters per second.Find dy/dt when .A)
B)
C)
D)
E)
Question
Differentiate 
with respect to t (x and y are functions of t).
A)
B)
C)
D)
E)
with respect to t (x and y are functions of t).A)
B)
C)
D)
E)
Question
The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r = 9 inches.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Find the rate of change of the distance D between the origin and a moving point on the graph of 
if 
centimeters per second.
A)
B)
C)
D)
E)
if centimeters per second.A)
B)
C)
D)
E)
Question
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground (see figure). When he is 10 feet from the base of the light, at what rate is the length of his shadow changing? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Full screen (f)
Deck 5: Differentiation
1
Describe the x-values at which the graph of the function given below is differentiable.
A) is differentiable on the interval .
B) is differentiable on the interval .
C) is differentiable everywhere except at .
D) is differentiable everywhere except at .
E) is differentiable at .
given below is differentiable. A)
is differentiable on the interval .B)
is differentiable on the interval .C)
is differentiable everywhere except at .D)
is differentiable everywhere except at .E)
is differentiable at . is differentiable everywhere except at . 2
Find the derivative of the function using the limiting process.
A)
B)
C)
D)
E)
using the limiting process.A)
B)
C)
D)
E)
3
Find an equation of the a line that is tangent to the graph of f and parallel to the given line.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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5
Find the derivative of the function by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
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6
Find the derivative of the following function using the limiting process.
A)
B)
C)
D)
E)
using the limiting process.A)
B)
C)
D)
E)
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7
Find an equation of the line that is tangent to the graph of the function and parallel to the line .
A)
B)
C)
D)
E)
and parallel to the line .A)
B)
C)
D)
E)
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8
Find the derivative of the function by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
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9
Find the slope m of the line tangent to the graph of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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10
Find the derivative of the following function using the limiting process.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Use the alternative form of the derivative to find the derivative of the function at .
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
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12
Find an equation of the line that is tangent to the graph of the function and parallel to the line .
A)
B)
C)
D)
E)
and parallel to the line .A)
B)
C)
D)
E)
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13
Find an equation of the tangent line to the graph of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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14
The graph of the function f is given below. Select the graph of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Find the derivative of the following function using the limiting process.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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16
Find the slope m of the line tangent to the graph of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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17
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
18
Find the derivative of the function by the limit process.
A)
B)
C)
D)
E)
by the limit process.A)
B)
C)
D)
E)
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19
Find an equation of the tangent line to the graph of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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20
Use the alternative form of the derivative to find the derivative of the function at .
A)
B)
C)
D)
E)
at .A)
B)
C)
D)
E)
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21
A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The position function is .What is its velocity after 4 seconds?
A)The velocity after 4 seconds is 128.4 meters per second.
B)The velocity after 4 seconds is -167.6 meters per second.
C)The velocity after 4 seconds is -187.2 meters per second.
D)The velocity after 4 seconds is 108.8 meters per second.
E)The velocity after 4 seconds is 276.4 meters per second.
.What is its velocity after 4 seconds?A)The velocity after 4 seconds is 128.4 meters per second.
B)The velocity after 4 seconds is -167.6 meters per second.
C)The velocity after 4 seconds is -187.2 meters per second.
D)The velocity after 4 seconds is 108.8 meters per second.
E)The velocity after 4 seconds is 276.4 meters per second.
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22
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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23
Find the slope of the graph of the function at the given value. when
A)
B)
C)
D)
E)
when A)
B)
C)
D)
E)
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24
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1364 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A)2.308 sec
B)8.957 sec
C)2.172 sec
D)8.711 sec
E)9.233 sec
. A silver coin is dropped from the top of a building that is 1364 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.A)2.308 sec
B)8.957 sec
C)2.172 sec
D)8.711 sec
E)9.233 sec
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25
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A)
B) and
C) and
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
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26
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval .
A)-70 ft/sec
B)98 ft/sec
C)-98 ft/sec
D)70 ft/sec
E)-107 ft/sec
. A silver coin is dropped from the top of a building that is 1378 feet tall. Determine the average velocity of the coin over the time interval .A)-70 ft/sec
B)98 ft/sec
C)-98 ft/sec
D)70 ft/sec
E)-107 ft/sec
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27
Suppose the position function for a free-falling object on a certain planet is given by is given by . A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.
A)
B)
C)
D)
E)
. A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.A)
B)
C)
D)
E)
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28
Use the Quotient Rule to differentiate the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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29
Use the Product Rule to differentiate .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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30
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A)
B) and
C) and
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
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31
A ball is thrown straight down from the top of a 250-ft building with an initial velocity of -12 ft per second. The position function is . What is the velocity of the ball after 4 seconds?
A)The velocity after 4 seconds is -280 ft per second.
B)The velocity after 4 seconds is -116 ft per second.
C)The velocity after 4 seconds is -140 ft per second.
D)The velocity after 4 seconds is -52 ft per second..
E)The velocity after 4 seconds is -76 ft per second.
. What is the velocity of the ball after 4 seconds?A)The velocity after 4 seconds is -280 ft per second.
B)The velocity after 4 seconds is -116 ft per second.
C)The velocity after 4 seconds is -140 ft per second.
D)The velocity after 4 seconds is -52 ft per second..
E)The velocity after 4 seconds is -76 ft per second.
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32
Find the derivative of the algebraic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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33
The length of a rectangle is and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.
A) square inches/second
B) square inches/second
C) square inches/second
D) square inches/second
E) square inches/second
and its height is , where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time.A)
square inches/secondB)
square inches/secondC)
square inches/secondD)
square inches/secondE)
square inches/second Unlock Deck
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34
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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k this deck
35
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.
A)-128.406 ft/sec
B)-256.811 ft/sec
C)-111.203 ft/sec
D)-267.298 ft/sec
E)-244.811 ft/sec
. A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.A)-128.406 ft/sec
B)-256.811 ft/sec
C)-111.203 ft/sec
D)-267.298 ft/sec
E)-244.811 ft/sec
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36
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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37
Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when .
A)-15 ft/sec
B)-45 ft/sec
C)-29 ft/sec
D)-30 ft/sec
E)-44 ft/sec
. A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when .A)-15 ft/sec
B)-45 ft/sec
C)-29 ft/sec
D)-30 ft/sec
E)-44 ft/sec
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38
Use the rules of differentiation to find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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39
Find the derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 77 flashcards in this deck.
Unlock Deck
k this deck
40
Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
A)
B) and
C) and
D)
E)The graph has no horizontal tangents.
A)
B)
and C)
and D)
E)The graph has no horizontal tangents.
Unlock Deck
Unlock for access to all 77 flashcards in this deck.
Unlock Deck
k this deck
41
Find dy/dx by implicit differentiation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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42
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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43
A population of 420 bacteria is introduced into a culture and grows in number according to the equation where t is measured in hours. Find the rate at which the population is growing when t = 5. Round your answer to two decimal places.
A)25.72 bacteria per hour
B)23.01 bacteria per hour
C)31.70 bacteria per hour
D)52.65 bacteria per hour
E)7.25 bacteria per hour
where t is measured in hours. Find the rate at which the population is growing when t = 5. Round your answer to two decimal places.A)25.72 bacteria per hour
B)23.01 bacteria per hour
C)31.70 bacteria per hour
D)52.65 bacteria per hour
E)7.25 bacteria per hour
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44
Evaluate for the equation at the given point Round your answer to two decimal places.
A)
B)
C)
D)
E)
for the equation at the given point Round your answer to two decimal places.A)
B)
C)
D)
E)
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45
Find the second derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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46
Find the second derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 77 flashcards in this deck.
Unlock Deck
k this deck
47
Find the derivative of the function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 77 flashcards in this deck.
Unlock Deck
k this deck
48
Find dy/dx by implicit differentiation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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k this deck
49
Find the second derivative of the function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
50
Evaluate the derivative of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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51
Find the derivative of the algebraic function .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
52
Evaluate the derivative of the function at the point .
A)
B)
C)
D)
E)
at the point .A)
B)
C)
D)
E)
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53
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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54
Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.
A)7.4 ft/sec2
B)0.4 ft/sec2
C)1.7 ft/sec2
D)0.8 ft/sec2
E)0.2 ft/sec2
where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.A)7.4 ft/sec2
B)0.4 ft/sec2
C)1.7 ft/sec2
D)0.8 ft/sec2
E)0.2 ft/sec2
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55
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
56
Evaluate for the equation at the given point Round your answer to two decimal places.
A)
B)
C)
D)
E)
for the equation at the given point Round your answer to two decimal places.A)
B)
C)
D)
E)
Unlock Deck
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k this deck
57
Find dy/dx by implicit differentiation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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58
Given the derivative below find the requested higher-order derivative. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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59
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
60
Evaluate the derivative of the function at the given point. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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61
Assume that x and y are both differentiable functions of t . Find for the equation
A)
B)
C)
D)
E)
for the equation A)
B)
C)
D)
E)
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62
Find d2y/dx2 in terms of x and y.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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63
A spherical balloon is inflated with gas at the rate of 200 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 60 centimeters?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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64
Find the points at which the graph of the equation has a vertical or horizontal tangent line.
A)There is a horizontal tangent at but no vertical tangents.
B)There is a horizontal tangent at and a vertical tangent at .
C)There is a vertical tangent at but no horizontal tangents.
D)There is a horizontal tangent at and a vertical tangent at .
E)There are no horizontal or vertical tangent lines.
A)There is a horizontal tangent at
but no vertical tangents.B)There is a horizontal tangent at
and a vertical tangent at .C)There is a vertical tangent at
but no horizontal tangents.D)There is a horizontal tangent at
and a vertical tangent at .E)There are no horizontal or vertical tangent lines.
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65
The radius, r, of a circle is increasing at a rate of 2 centimeters per minute.Find the rate of change of area, A, when the radius is .
A) sq cm/min
B) sq cm/min
C) sq cm/min
D) sq cm/min
E) sq cm/min
.A)
sq cm/minB)
sq cm/minC)
sq cm/minD)
sq cm/minE)
sq cm/min Unlock Deck
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66
A conical tank (with vertex down) is 20 feet across the top and 26 feet deep. If water is flowing into the tank at a rate of 16 cubic feet per minute, find the rate of change of the depth of the water when the water is 12 feet deep.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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67
Find in terms of x and y given that
A)
B)
C)
D)
E)
in terms of x and y given that A)
B)
C)
D)
E)
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68
Assume that x and y are both differentiable functions of t. Find for the equation
A)
B)
C)
D)
E)
for the equation A)
B)
C)
D)
E)
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69
A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changed when the base of the ladder is 8 feet from the wall. Round your answer to two decimal places.
A) ft2/sec
B) ft2/sec
C) ft2/sec
D) ft2/sec
E) ft2/sec
A)
ft2/secB)
ft2/secC)
ft2/secD)
ft2/secE)
ft2/sec Unlock Deck
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70
A man 6 feet tall walks at a rate of 13 feet per second away from a light that is 15 feet above the ground (see figure). When he is 8 feet from the base of the light, at what rate is the tip of his shadow moving?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
A ladder 20 feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of 4 feet per second. How fast is the top of the ladder moving down the wall when its base is 14 feet from the wall? Round your answer to two decimal places.
A)6.86 ft/sec
B)-6.00 ft/sec
C)-3.92 ft/sec
D)8.00 ft/sec
E)-6.86 ft/sec
A)6.86 ft/sec
B)-6.00 ft/sec
C)-3.92 ft/sec
D)8.00 ft/sec
E)-6.86 ft/sec
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72
A point is moving along the graph of the function such that dx/dt = 5 centimeters per second.Find dy/dt when .
A)
B)
C)
D)
E)
such that dx/dt = 5 centimeters per second.Find dy/dt when .A)
B)
C)
D)
E)
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73
Differentiate with respect to t (x and y are functions of t).
A)
B)
C)
D)
E)
with respect to t (x and y are functions of t).A)
B)
C)
D)
E)
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74
The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r = 9 inches.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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75
All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume changing when each edge is 5 centimeters?
A)150 cm3/sec
B)450 cm3/sec
C)300 cm3/sec
D)540 cm3/sec
E)180 cm3/sec
A)150 cm3/sec
B)450 cm3/sec
C)300 cm3/sec
D)540 cm3/sec
E)180 cm3/sec
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76
Find the rate of change of the distance D between the origin and a moving point on the graph of if centimeters per second.
A)
B)
C)
D)
E)
if centimeters per second.A)
B)
C)
D)
E)
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77
A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground (see figure). When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
Unlock for access to all 77 flashcards in this deck.
