Newton's method finds roots by iterating xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ). Starting from an initial guess x₀, each step uses the tangent line to approximate the root. Converges quadratically when near a root. May fail if f′(xₙ) = 0 or the initial guess is poor.
How to Use
Select a function and initial guess:
- Function: Choose from presets
- x₀: Initial guess
- Iterations: Watch convergence
Convergence
- Quadratic convergence near simple roots
- Linear near repeated roots
- May diverge for bad initial guesses
Why Derivatives?
The derivative f′(x) gives the tangent slope. The tangent line crosses zero at xₙ − f(xₙ)/f′(xₙ), providing the next approximation.
Step-by-Step Instructions
- 1Select a function.
- 2Enter initial guess x₀.
- 3Set tolerance.
- 4View iteration table.
- 5Check convergence.