Choose a polynomial and a starting point. Follow each exact tangent step, then inspect what the recorded run establishes.
A tangent intercept is the next iterate. Its residual tells you whether that point is an exact root.
Every completed point is retained. Select a point number to inspect its tangent. Fractions remain exact even when a short decimal display would round them.
| Point | x | f(x) | f′(x) |
|---|
Download the lesson JSON, open it in RecallWeave, inspect the preview and choose Start this deck. Keep the worked guide beside your experiment.
The start accepts integers, decimals with up to three decimal places, or fractions with a positive denominator at most 1000 and numerator magnitude at most 20000, within −20 to 20. The polynomial has four integer coefficients from −12 to 12. Choose 1–8 steps.
Every fraction and stopping decision is exact within a 4096-bit numerator/denominator bound. A resource stop preserves the last complete step and establishes no convergence or divergence. Plot coordinates and short decimal labels are approximate. Editing an input retires the previous record until you run again. This self-contained page makes no network requests.