Activity Overview
Visually see the geometry and calculus behind Newton's Method.
Objectives
- Visually see the geometry and calculus behind Newton's Method
About the Lesson
Newton's Method uses successive tangent line approximations to iteratively find zeroes of a function. The idea: starting with an initial guess x0 of a zero for the function f, one finds the zero for the tangent line approximation to the graph of f at (x0, f(x0)), namely the solution x = x1 to 0 = f'(x0)(x – x0) + f(x0), or equivalently . One then uses x1 as the next guess of a root and repeats the process until it converges.