Newtons Method: A Computer Project :: Newton-Raphson Method

norths system A Computer ProjectNewtons Method is used to find the first of an equation provided thatthe function fx is equal to zero. Newton Method is an equation created beforethe days of calculators and was used to find approximate roots to numbers. Theroots of the function are where the function crosses the x axis. The basic linguistic rule behind Newtons Method is that the root can be found by subtractingthe function divided by its derivative from the initial guess of the root.Newtons Method worked surface because an initial guess was given to putinto the equation. This is important because a wrong initial guess may give youthe wrong root for the function. With Mathematica, a course for Newtonsmethod can be produced and a graph of the function can be made. From the graph,the a good initial guess can be made.Although Newtons Method works to find roots for many functions, it doeshave its disadvantages. The root just abouttimes cannot be found by using NewtonsMethod. The re ason it sometimes cannot be found is because when the function isequal to zero, there is no slope to the tangent line.As seen in experimentations, it is important to select an initial guessclose to the root because some functions have multiple roots. Failure to choosean initial value that is close to the root could result in finding a the wrongroot or wasting a lot of time doing multiple iterations while getting close tothe actual root.On some occasions, the program cannot find a root to an initial guessthat is placed into the program. In some instances Mathmatica could not findthe root to the function, like if it is a parabola with its vertex is placed