Chat with AI
Deck 3: Section 7: Differentiation
Full screen (f)
Question
A point is moving along the graph of the function 
such that 
centimeters per second. Find 
when x = 
.
A)
B)
C)
D)
E)
such that centimeters per second. Find when x = .A)
B)
C)
D)
E)
Question
A man 6 feet tall walks at a rate of 
feet per second away from a light that is 15 feet above the ground (see figure). When he is 
feet from the base of the light, at what rate is the tip of his shadow moving? 
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the tip of his shadow moving? A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Question
A ladder 
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 
feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 
feet from the wall. Round your answer to three decimal places. 
A)
rad/sec
B)
rad/sec
C)
rad/sec
D)
rad/sec
E)
rad/sec
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 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is feet from the wall. Round your answer to three decimal places. A)
rad/secB)
rad/secC)
rad/secD)
rad/secE)
rad/sec Question
Find the rate of change of the distance 
between the origin and a moving point on the graph of 
if 
centimeters per second.
A)
B)
C)
D)
E)
between the origin and a moving point on the graph of if centimeters per second.A)
B)
C)
D)
E)
Question
A conical tank (with vertex down) is 
feet across the top and 
feet deep. If water is flowing into the tank at a rate of 
cubic feet per minute, find the rate of change of the depth of the water when the water is 
feet deep.
A)
B)
C)
D)
E)
feet across the top and feet deep. If water is flowing into the tank at a rate of cubic feet per minute, find the rate of change of the depth of the water when the water is feet deep.A)
B)
C)
D)
E)
Question
All edges of a cube are expanding at a rate of 
centimeters per second. How fast is the volume changing when each edge is 
centimeters?
A)
B)
C)
D)
E)
centimeters per second. How fast is the volume changing when each edge is centimeters?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
An airplane is flying in still air with an airspeed of 
miles per hour. If it is climbing at an angle of 
, find the rate at which it is gaining altitude. Round your answer to four decimal places.
A)
B)
C)
D)
E)
miles per hour. If it is climbing at an angle of , find the rate at which it is gaining altitude. Round your answer to four decimal places.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 
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 
feet per second. How fast is the top of the ladder moving down the wall when its base is 
feet from the wall? Round your answer to two decimal places. 
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
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 feet per second. How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places. A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Question
The radius, r, of a circle is decreasing at a rate of 
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
centimeters per minute. Find the rate of change of area, A, when the radius is .A)
sq cm/minB)
sq cm/minC)
sq cm/minD)
sq cm/minE)
sq cm/min Question
The radius r of a sphere is increasing at a rate of 
inches per minute. Find the rate of change of the volume when r = 
inches.
A)
B)
C)
D)
E)
inches per minute. Find the rate of change of the volume when r = inches.A)
B)
C)
D)
E)
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 ladder 
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 
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 
feet from the wall. Round your answer to two decimal places. 
A)
B)
C)
D)
E)
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 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 feet from the wall. Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
A man 6 feet tall walks at a rate of 
feet per second away from a light that is 15 feet above the ground (see figure). When he is 
feet from the base of the light, at what rate is the length of his shadow changing? 
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the length of his shadow changing? A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Question
A spherical balloon is inflated with gas at the rate of 
cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 
centimeters?
A)
B)
C)
D)
E)
cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is centimeters?A)
B)
C)
D)
E)
Unlock Deck
Sign up to unlock the cards in this deck!
Unlock Deck
Unlock Deck
1/16
Play
Full screen (f)
Deck 3: Section 7: Differentiation
1
A point is moving along the graph of the function such that centimeters per second. Find when x = .
A)
B)
C)
D)
E)
such that centimeters per second. Find when x = .A)
B)
C)
D)
E)
2
A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the tip of his shadow moving?
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the tip of his shadow moving? A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec ft/sec 3
A ladder 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 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is feet from the wall. Round your answer to three decimal places.
A) rad/sec
B) rad/sec
C) rad/sec
D) rad/sec
E) rad/sec
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 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is feet from the wall. Round your answer to three decimal places. A)
rad/secB)
rad/secC)
rad/secD)
rad/secE)
rad/sec rad/sec 4
Find the rate of change of the distance between the origin and a moving point on the graph of if centimeters per second.
A)
B)
C)
D)
E)
between the origin and a moving point on the graph of if centimeters per second.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
5
A conical tank (with vertex down) is feet across the top and feet deep. If water is flowing into the tank at a rate of cubic feet per minute, find the rate of change of the depth of the water when the water is feet deep.
A)
B)
C)
D)
E)
feet across the top and feet deep. If water is flowing into the tank at a rate of cubic feet per minute, find the rate of change of the depth of the water when the water is feet deep.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
6
All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume changing when each edge is centimeters?
A)
B)
C)
D)
E)
centimeters per second. How fast is the volume changing when each edge is centimeters?A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
7
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)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
8
An airplane is flying in still air with an airspeed of miles per hour. If it is climbing at an angle of , find the rate at which it is gaining altitude. Round your answer to four decimal places.
A)
B)
C)
D)
E)
miles per hour. If it is climbing at an angle of , find the rate at which it is gaining altitude. Round your answer to four decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
9
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)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
10
A ladder 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 feet per second. How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places.
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
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 feet per second. How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places. A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
11
The radius, r, of a circle is decreasing at a rate of 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
centimeters per minute. Find the rate of change of area, A, when the radius is .A)
sq cm/minB)
sq cm/minC)
sq cm/minD)
sq cm/minE)
sq cm/min Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
12
The radius r of a sphere is increasing at a rate of inches per minute. Find the rate of change of the volume when r = inches.
A)
B)
C)
D)
E)
inches per minute. Find the rate of change of the volume when r = inches.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
13
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)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
14
A ladder 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 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 feet from the wall. Round your answer to two decimal places.
A)
B)
C)
D)
E)
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 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 feet from the wall. Round your answer to two decimal places. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
15
A man 6 feet tall walks at a rate of feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the length of his shadow changing?
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
feet per second away from a light that is 15 feet above the ground (see figure). When he is feet from the base of the light, at what rate is the length of his shadow changing? A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
16
A spherical balloon is inflated with gas at the rate of cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is centimeters?
A)
B)
C)
D)
E)
cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is centimeters?A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 16 flashcards in this deck.
