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

A particle moves along the -axis with its position at time given by , where and are non-zero constants and .

For which of the following values of is the particle at rest?

For , the position of a particle moving along the -axis is given by . What is the velocity of the particle at the point where the acceleration is first equal to 0?

If the base of a triangle is increasing at a rate of 12 centimeters per second while its height is decreasing at a rate 12 centimeters per second, which of the following must be true about the area of the triangle?

The radius of a right circular cylinder is increasing at a rate of 4 units per second. The height of the cylinder is decreasing at a rate of 6 units per second.

Which of the following expressions gives the rate at which the volume of the cylinder is changing with respect to time in terms of the radius and height of the cylinder?

(The volume of a cylinder with radius and height is .)