Related Rates

Ships Sailing Away

A GeoGebra simulator - giving all of the construction and mathematics - for thinking about the related rates problems of ships moving in different directions and at different speeds.

Sample Problem: At noon, ship A is 90 km west of ship B. Ship A is sailing south at 40 km/h and ship B is sailing north at 20 km/h. How fast is the distance between the ships changing at 2:00 PM?

Emptying Cone Problem

• Animated Visualization - by Richard Hickey and LFS (No math yet, but one can see how the cone empties slowly and then faster and faster as the jar fills linearly.)

Extrema

Box-Folding Problem

A GeoGebra simulator for the folding box - extreme value problem.

Sample Problem: A rectangular piece of cardboard measures 4" by 6". Equal sized squares are to be cut out of each corner and the sides folded up to make a box (no top). What should be the length of the sides of the squares to maximize the volume of the box?

Graphical methods

GeoGebra is also suitable for solving calculus problems by Graphical methods described in that dedicated page.