Rates of Change & Related Rates (College Board AP® Calculus AB)

Léon swims back and forth along a straight path in a 50-meter-long pool for 126 seconds. Léon's velocity is modeled by , where is measured in seconds and is measured in meters per second.

Find all times in the interval at which Léon changes direction. Give a reason for your answer.

Find Léon's acceleration at time seconds and indicate units of measure. Is Léon speeding up or slowing down at time seconds? Give a reason for your answer.

The height of a cone increases at a rate of 3 centimeters per hour whilst the radius increases at a rate of 1 centimeter per hour. At time hours, the radius is 300 centimeters and the height is 100 centimeters. Find the rate of change of the volume of the cone with respect to time in cubic centimeters per hour, at time hours. (The volume of a cone with radius and height is .)

A young animal's weight, in kilograms, can be modeled by the function , where is the animal's length in centimeters. When the animal weighs 4 kilograms, its length is increasing at a rate of 3 centimeters per month.

According to this model, what is the rate of change of the animal's weight with respect to time, in kilograms per month, at the time when the animal is 4 kilograms?

Particle moves along the -axis such that, for time , its velocity is given by .

Find all times , when the speed of the particle is decreasing. Justify your answer.