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# 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.

This online calculator implements Newton's method (also known as the Newton–Raphson method) using derivative calculator to obtain analytical form of derivative of given function, because this method requires it. Some theory to recall the method basics can be found below the calculator. #### Newton's method

Digits after the decimal point: 4
Function

Derivative

x

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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.