Introduction

This Section is concerned with the problem of “root location”; i.e. finding those values of $x$ which satisfy an equation of the form $f\left(x\right)=0$ . An initial estimate of the root is found (for example by drawing a graph of the function). This estimate is then improved using a technique known as the Newton-Raphson method, which is based upon a knowledge of the tangent to the curve near the root. It is an “iterative” method in that it can be used repeatedly to continually improve the accuracy of the root.

Prerequisites

• be able to differentiate simple functions
• be able to sketch graphs

Learning Outcomes

• distinguish between simple and multiple roots
• estimate the root of an equation by drawing a graph
• employ the Newton-Raphson method to improve the accuracy of a root