Principles of Calculus Name__________________________

Unit 6 Day 4: Intro to Related Rates HW Date______________________

For problems 1-4, assume that x and y are both differentiable functions of t and find the required values of

dy/dt and dx/dt.

1) Given dx/dt = 3 and the equation y x , find dy/dt when x = 4.

2) Given dy/dt = 2 and the equation y x , find dx/dt when x = 25.

3) Given dx/dt = 10 and the equation xy = 4, find dy/dt when x = 8. (Toward the end, remember that

if you know xy = 4, you can easily solve for y.)

4) Given dy/dt = -6 and the equation xy = 4, find dx/dt when x = 1.

5) A point is moving along the graph of the function y = sin x such that dx/dt is 2 centimeters per

second. Find dy/dt to the nearest hundredth for each of the specified values.

a) x = -1

b) x = 0

c) x = 1

d) x = 3

Principles of Calculus Name__________________________

Unit 6 Day 4: Intro to Related Rates HW Date______________________

6) The radius r of a circle is increasing at a rate of 2 centimeters per minute. Find the rate of change of

the area when…

a) …r = 6 centimeters?

b) …r = 24 centimeters?

7) All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume

changing when each edge is …

a) …1 centimeter?

b) …10 centimeters?

8) A spherical ball is inflated with air at the rate of 500 cubic centimeters per minute. How fast is the

radius of the balloon increasing at the instant …

a) …the radius is 30 centimeters?

b) …the radius is 60 centimeters?

9) A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away

from the wall at a rate of 2 feet per second. How fast is the top moving down the wall when the base

of the ladder is …

a) …7 feet from the wall?

b) …15 feet from the wall?

c) …24 feet from the wall?

25 ft