Newton's Method
Root-finding you can see. Newton's method slides down each tangent line to the x-axis and lands closer to a root every step.
Newton's Method VisualizerLive
root finding · tangent iterations
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Newton's method slides down each tangent line to the x-axis, homing in on a root.
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Root2.094551
Iterations6
Convergencequadratic
Governing equation
Reading this result: Starting at x0 = 3, Newton reached x ≈ 2.094551 in 6 steps. This is a simple root where f'(x) is well away from zero, so the error roughly squares each step (quadratic convergence) — the number of correct digits doubles per iteration.
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How it works
Given f(x), Newton's method iterates x → x − f(x)/f′(x). PolySim's CAS computes the derivative symbolically, and each tangent step is drawn so you can watch the quadratic convergence — and see how a bad starting guess can send it astray.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.