Newton's method (or the Newton-Raphson method) is a simple iterative numerical method to approximate roots of equations: Given one approximation, the idea is to go up to the graph, and then slide down the tangent to the x-axis to obtain the next approximation. In symbols, the sequence of approximate roots x0, x1, x2, x3, ... is created by the rule
-> Try various initial points to compare how quickly a true
root is approached.
-> Note that it is harder to approach "middle" roots than the largest and smallest.
-> See Pathological Example to see what can go wrong.