Unit 4: Contextual Applications of Differentiation

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

A spherical balloon is being inflated so that its volume increases at a rate of [math] cm[math]/sec. How fast is the radius increasing when the radius is [math] cm?

Evaluate [math].

Use a linear approximation of [math] at [math] to estimate [math]. Give your answer as a decimal.

If [math] on the interval [math], find the value of [math] guaranteed by the Mean Value Theorem. Give an exact decimal answer.

A 10-foot ladder leans against a wall. The bottom slides away from the wall at 2 ft/sec. How fast is the top sliding down when the bottom is 6 ft from the wall? Give your answer as a fraction.

A particle's position is [math] for [math]. What is the acceleration at [math]?

A particle moves along the [math]-axis with velocity [math]. At [math], is the speed of the particle increasing or decreasing?

The temperature [math] of a cup of coffee (in °F) [math] minutes after being poured satisfies [math]. What does this mean?

A particle has velocity [math] for [math]. What is the total distance traveled by the particle over this interval?

A spherical balloon is being inflated so that its volume increases at a rate of [math] cm[math]/s. At the instant when the radius is 5 cm, how fast is the radius increasing?

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

Use the linearization of [math] at [math] to approximate [math]. Express your answer as a fraction.

Let [math] on [math]. Find the value of [math] guaranteed by the Mean Value Theorem.

A 10-foot ladder leans against a wall. The bottom slides away at 2 ft/s. When the bottom is 6 ft from the wall, how fast (in ft/s) is the top sliding down? Express your answer as a fraction.

Evaluate [math]. Express your answer as a fraction.

A particle moves along the [math]-axis with position [math]. What is the speed of the particle at [math]?

A farmer has 200 ft of fencing to enclose a rectangular pen against a barn (no fencing needed along the barn). What is the maximum area of the pen?

The position of a car at time [math] hours is [math] miles. What is the average velocity from [math] to [math] in miles per hour?

A spherical balloon is inflated so that its radius increases at a rate of 2 cm/s. At the instant when the radius is 5 cm, at what rate is the volume increasing?