Hi, Today we'll learn about Newton-Raphson Method " Newton's Method ". this method is for finding successively better approximate solutions to the roots of a function (real valued). so are you ready for this............you will. Newton's Method: The Newton's method is one of the most powerful and well known method used for finding a root of f(X) = 0 there are many ways to derive Newton-Raphson method . the simplest way to derive this formula is by using the first two terms in the Taylor series expansion of the form. Instead of working with the chord joining points on the graph of y= f(X) as in bisection method and false position method s. Newton's method uses the tangent at one point on the graph of y= f(X) therefor it requires only one instead of two initial guesses. Suppose X is an initial guesses draw the tangent line at X= X0 and procedure it to meet the X - axis at X = X1 Newton's Method which shows in picture above. now from righ