Newton's Method

Interactive visualization of the Newton–Raphson root-finding algorithm

f(x) Tangent Vertical drop Root approx.
Click to set x₀ · Drag to pan · Scroll to zoom
nxₙf(xₙ)f′(xₙ)|xₙ − xₙ₋₁|

Newton's Method

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

Starting from an initial guess $x_0$, each iteration approximates the root by following the tangent line of $f$ at $(x_n, f(x_n))$ to its $x$-intercept.