Newton-Raphson method explorer

This demo shows how the Newton-Raphson root-finding algorithm works, using a few selected 1-D functions. You can pick a function and a starting point for the algorithm, as well as the values of the parameters $\epsilon$ and $\delta$ to use to declare convergence, and see how you get closer to a root with each step of the algorithm. You can click and drag a box around an area to zoom into it (useful as you get closer to a root), and double click/tap to zoom out. At the bottom of the demo, you can see plots showing the evolution of $x_n$, $x_{n+1}$, $f(x_n)$, and $f(x_{n+1})$ with iterations.

At each step, the next 'guess' for the root, $x_{n+1}$ is computed by finding the point where the tangent line at $f(x_n)$ intersects the $x$-axis.

Update rule $$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$$

Current point $x_n$

Previous iterations

Next point $x_{n+1}$

Function

$f(x)$

Starting point $x_0$

Convergence

$|f(x_n)|$ < ε

10⁻⁸

$|x_{n+1} - x_n|$ < δ

10⁻⁸

Current state

Step

—

$x_n$

—

$f(x_n)$

—

$f'(x_n)$

—

$x_{n+1}$

—

Evolution over iterations

$x_n$ and $x_{n+1}$

$f(x_n)$

$f'(x_n)$

Created by Adarsh Pyarelal with assistance from Claude · INFO 521, Spring 2026 · University of Arizona