# Newton's method

This online calculator implements Newton's method (also known as the Newton–Raphson method) for finding the roots (or zeroes) of a real-valued function.

It implements Newton's method using derivative calculator to obtain an analytical form of the derivative of a given function because this method requires it. You can find a theory to recall the method basics below the calculator. #### Newton's method

Digits after the decimal point: 4
Function

Derivative

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### Newton–Raphson method1

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

The method starts with a function f defined over the real numbers x, the function's derivative f ′, and an initial guess x0 for a root of the function f. If the function satisfies the assumptions made in the derivation of the formula and the initial guess is close, then a better approximation x1 is

Geometrically, (x1, 0) is the intersection of the x-axis and the tangent of the graph of f at (x0, f(x0)).

The process is repeated as , until a sufficiently accurate value is reached.