Newton’s Method

Ride the tangent

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Newton: $x_{n+1} = x_n - f(x_n)/f'(x_n)$, using the tangent line.
• Near a root, correct digits roughly double each step (quadratic convergence).
• Bad starting points can make Newton’s method cycle or fail.

Steps

1. Follow the tangent line
2. Tangent steps
3. One step by hand
4. Overshoot
5. Cube root of 10
6. When Newton fails