Unit 4: Contextual Applications of Differentiation

A particle moves with position [math]. What is the speed at any time [math]?

A spherical balloon is being inflated so that its volume increases at a constant rate of [math]. When the radius is [math] cm, the rate at which the radius is increasing is

A particle moves along the [math]-axis with velocity [math] for [math]. The total distance traveled by the particle from [math] to [math] is

The linear approximation of [math] at [math] gives an approximate value of [math] equal to

A 13-foot ladder leans against a wall. The foot of the ladder slides away from the wall at [math] ft/s. When the foot is [math] feet from the wall, the top of the ladder is sliding down the wall at

If [math] represents position (in meters), the velocity at [math] second is

Water pours into a conical tank at [math]. The tank has height [math] m and radius [math] m at the top. When the water level is [math] m high, the rate at which the water level rises is

A sphere's radius increases at [math] cm/s. How fast is the volume changing when [math] cm? ([math])

A 10-foot ladder slides down a wall. The base moves away at 1 ft/s. How fast is the top sliding down when the base is 6 ft from the wall?

A particle has acceleration [math] and [math]. What is [math]?

Water fills a cone (height 10 m, radius 5 m) at 3 m³/min. How fast is the depth rising when [math] m? ([math], [math])

The position of a particle is [math]. What is the acceleration?

A rectangle has perimeter 20. What dimensions maximize the area?

A particle moves with [math]. Find the total distance traveled from [math] to [math].

A particle moves along the x-axis with velocity [math] for [math]. On which interval(s) is the particle moving to the left?