Beginning of Essay
Newton's Method is used to find the root of an equation provided that the function f[x] is equal to zero. Newton Method is an equation created before the days of calculators and was used to find approximate roots to numbers. The roots of the function are where ....

Middle of Essay
.... is equal to zero, there is no slope to the tangent line. As seen in experimentation's, it is important to select an initial guess close to the root because some functions have multiple roots. Failure to choose an initial value that is close to the root could result in finding a the wrong root or wasting a lot of time doing multiple iterations while getting close to the actual root. On some occasions, the program cannot find a root to an initial guess that is placed into the program. In some instances Mathmatica could not find the root to the function, like if it is a parabola with its vertex is placed right on the y axis with its roots an e ....