Unit 4: Contextual Applications of Differentiation

A particle moves along the x-axis so that its position at time [math] is given by [math].

A conical tank has height [math] ft and radius [math] ft at the top. Water flows in at [math] ft[math]/min. The volume of a cone is [math].

A rectangle has a length [math] that is increasing at [math] cm/s and a width [math] that is decreasing at [math] cm/s. At a certain time, [math] cm and [math] cm.

The function [math] is twice differentiable with [math], [math], and [math].

A [math]-foot ladder leans against a wall. The bottom slides away from the wall at [math] ft/s.

A particle moves along the [math]-axis with velocity [math] for [math].

A spherical balloon is being inflated. The volume increases at a constant rate of [math] cm[math]/s.

A farmer has [math] meters of fencing and wants to enclose a rectangular area along a river (no fence needed on the river side).

A person [math] feet tall walks away from a [math]-foot streetlight at [math] ft/s.

A car travels along a highway. Its position [math] in miles at time [math] hours is recorded: