Name _____________________________
Period _____ Date ________________
Additional Practice Problems Can Be Found in Section 4.1 of your Online Textbook
dx
(1) A particle travels along the curve y = x . At the moment when the particle is at (9, 3), it is given that =7
dt
dy
units per second. Find at the same moment.
dt
dx
(2) A particle travels along the curve y = cos x in such a way that dt
is always 2 units per second.
dy
As the particle travels through some point P, we have = 3 . Find all possible x-coordinates of point P (given
dt
0 x 2 ) , then find the corresponding y-coordinate for each point.
(3) The side length of a square increases at a constant rate of 5 cm/sec. At the moment when the square’s area is
36 cm2, find the rate of change, with respect to time, of the square’s area. Indicate units of measure in your answer.
This study source was downloaded by 100000899606070 from CourseHero.com on 06-19-2025 09:58:22 GMT -05:00
https://www.coursehero.com/file/174903058/HW3-Related-Ratespdf/
, (4) The volume of a cube decreases at a constant rate of 1 ft3/min. At the moment when the cube’s volume is 27 ft3,
find the following.
a. Find the rate of change, with respect to time, of the length of one of the cube’s edges. Include units.
b. Find the rate of change, with respect to time, of the cube’s surface area. Include units in your answer.
(5) A trough is 12 feet long and 3 feet across the top. Its ends are isosceles triangles with altitudes of 3 feet.
a. For part (a) only, suppose water is being pumped into the trough at a constant rate 3 ft
of 2 cubic feet per minute. How fast is the water level rising when the depth h is 12 ft
1 foot? Include units of measure in your answer.
h ft
3 ft
a. For part (b) only, suppose the water is rising at a rate of 3/8 inch per minute when 3 ft
h = 2 feet. Find the rate at which water is being pumped into the trough. Include 12 ft
units of measure in your answer.
h ft
3 ft
This study source was downloaded by 100000899606070 from CourseHero.com on 06-19-2025 09:58:22 GMT -05:00
https://www.coursehero.com/file/174903058/HW3-Related-Ratespdf/
Period _____ Date ________________
Additional Practice Problems Can Be Found in Section 4.1 of your Online Textbook
dx
(1) A particle travels along the curve y = x . At the moment when the particle is at (9, 3), it is given that =7
dt
dy
units per second. Find at the same moment.
dt
dx
(2) A particle travels along the curve y = cos x in such a way that dt
is always 2 units per second.
dy
As the particle travels through some point P, we have = 3 . Find all possible x-coordinates of point P (given
dt
0 x 2 ) , then find the corresponding y-coordinate for each point.
(3) The side length of a square increases at a constant rate of 5 cm/sec. At the moment when the square’s area is
36 cm2, find the rate of change, with respect to time, of the square’s area. Indicate units of measure in your answer.
This study source was downloaded by 100000899606070 from CourseHero.com on 06-19-2025 09:58:22 GMT -05:00
https://www.coursehero.com/file/174903058/HW3-Related-Ratespdf/
, (4) The volume of a cube decreases at a constant rate of 1 ft3/min. At the moment when the cube’s volume is 27 ft3,
find the following.
a. Find the rate of change, with respect to time, of the length of one of the cube’s edges. Include units.
b. Find the rate of change, with respect to time, of the cube’s surface area. Include units in your answer.
(5) A trough is 12 feet long and 3 feet across the top. Its ends are isosceles triangles with altitudes of 3 feet.
a. For part (a) only, suppose water is being pumped into the trough at a constant rate 3 ft
of 2 cubic feet per minute. How fast is the water level rising when the depth h is 12 ft
1 foot? Include units of measure in your answer.
h ft
3 ft
a. For part (b) only, suppose the water is rising at a rate of 3/8 inch per minute when 3 ft
h = 2 feet. Find the rate at which water is being pumped into the trough. Include 12 ft
units of measure in your answer.
h ft
3 ft
This study source was downloaded by 100000899606070 from CourseHero.com on 06-19-2025 09:58:22 GMT -05:00
https://www.coursehero.com/file/174903058/HW3-Related-Ratespdf/
