*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
x_{0}, x_{1}, x_{2}, x_{3}, ... 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.