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## Calculus

Add your Calculus materials here, please use the following form to do this:

- Pythagoras, Download

Visualization of Pythagoras' theorem by Markus Hohenwarter

## Contents |

# 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.

Directions and Good Questions or TMA Article Abstract

**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?

- Related topics: Calculus with GeoGebra
- Keywords: related rates, calculus, speed, simulator LFS

## Oil Spill Problem

- Animated Visualization - by Richard Hickey and LFS

## 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?

- Related topics: Calculus with GeoGebra
- Keywords: extreme values, extrema, calculus, simulator LFS

# Graphical methods

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