# Applications of Differentiation

by M. Bourne

## Introduction to Applications of Differentiation

In Isaac Newton's day, one of the biggest problems was poor **navigation at sea**.

Before calculus was developed, the stars were vital for navigation.

Shipwrecks occured because the ship was not where the captain thought it should be. There was not a good enough understanding of how the Earth, stars and planets moved with respect to each other.

**Calculus** (differentiation and integration) was developed to improve this understanding.

Differentiation and integration can help us solve many types of **real-world problems**.

We use the **derivative** to determine the **maximum and minimum values** of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).

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We meet derivatives in many **engineering and science problems**, especially when modelling the behaviour of moving objects.

Our discussion begins with some general applications which we can then apply to specific problems.

We begin with 1. Tangents and Normals »

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