Newton's Method Visualizer: Cookie Club

What is happening here?

You want to solve f(x) = 0, the spot where a curve crosses the x-axis. Some equations have no formula for that spot, so you guess and let each guess teach you a better one. Stand on the curve at your guess, draw the tangent line (the straight line that just kisses the curve there), and follow it down to the x-axis. That crossing is your next guess. Repeat, and watch the guesses home in.

x_n+1 = x_n − f(x_n) / f′(x_n)

In plain words: nudge your guess by the function's value divided by its slope. Steep slope, small careful step. Far from zero, big stride. The formula picks its own step size, which is why it can be so fast.

1. Pick a curve

Or type your own polynomial: Use x, numbers, +, −, *, and ^ for powers. Example: 2*x^3 - 4*x + 1

2. Pick a starting guess

x₀ =

Tip: you can also click (or tap) anywhere on the plot to drop your starting guess there.

Skip animation (instant steps)

3. Watch it work

Press "Step once" to take your first Newton step, or hit Auto-play and watch the tangent lines do the walking.

Iteration table

Each row is one round of guess-and-improve.
n	x_n	f(x_n)	error vs root
No steps yet. Your guesses will appear here.

Ways to break it (on purpose)

Go flat: start where the curve is nearly horizontal and the tangent has nowhere to go. Newton hates flat spots.
Bounce: try the troublemaker curve starting at exactly 0. Some guesses never settle down.
Fly away: start absurdly far from any crossing and watch the first tangent launch your guess into orbit.
Count the digits: on x² − 2, watch how many correct digits you gain per step. They roughly double. That is quadratic convergence, the magic trick inside the magic trick.