How to use it
- Enter f(x) so that the equation is f(x) = 0.
- Give a starting guess near the root you want.
- Read the root and the step table. Each row shows x and f(x).
How it works
The tool differentiates f symbolically, then repeats x ← x − f(x) / f′(x). It stops when |f(x)| is at most the tolerance, or when a step moves x by no more than the tolerance (relative to 1 + |x|), or when the iteration limit is reached.
Worked example
Solve x² − 2 = 0 from x₀ = 1. Then f′(x) = 2x and:
- x₁ = 1 − (−1) / 2 = 1.5
- x₂ = 1.5 − 0.25 / 3 = 1.4166667
- x₃ = 1.4142157, x₄ = 1.4142136 ≈ √2
Tips
- Plot or evaluate f first to pick a guess near the root.
- A guess where f′ is zero or tiny can throw the iteration far away.