Newton's Method : If x_{n }is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x_{n} ) ≠ 0 the next approximation is given by
x_{n+1 }= x_{n} - f(x_{n})/f'(x_{n})
It has to lead to the question of while do we stop? How several times do we go through this procedure? One of the more common stopping points in the procedure is to continue till two successive approximations agree upon a given number of decimal places.