Title: 12_3 The Newton–Raphson Method
Course: HELM Workbooks 2023-2024 > Section: HELM 12: Applications of Differentiation

This Section is concerned with the problem of “root location”; i.e. finding those values of \(x\) which satisfy an equation of the form \(f(x)=0\). 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.