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 »