Calculus & Numerical Methods
Newton-Raphson Root
Find a root of f from an initial guess.
Formula
Formula
xn+1 = xn − f(xn)f'(xn)
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| f | function | expression / text | x | input |
| x₀ | initial guess | computed result | — | result |
Try it yourself
Interactive calculator
Worked examples
Example 1
Givenf(x) = x*x - 2, guess x₀ = 1
Result1.414213562
Example 2
Givenf(x) = cos(x) - x, guess x₀ = 1
Result0.7390851332