This handy online calculator implements Newton’s method (also known as the Newton–Raphson method) using a derivative calculator to obtain analytical form of derivative of any given function, because this method calls for it.
Some theory to recall the method basics can be found written below the calculator. In numerical analysis, this method was obviously named after Isaac Newton and Joseph Raphson and is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
The method begins 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 is able to satisfy the assumptions made in the derivation of the formula and the initial guess is close, then a better approximation x1 is:
x1 = x0 – f(x0)f'(x0)
Newton’s method is an extremely powerful and one of a kind technique. Generally, the convergence is quadratic as the method converges on the root, the difference between the root and the approximation is squared off (the number of accurate digits roughly doubles) at each step.