An iterative process using derivatives that can often (but not always) be used to find zeros of a differentiable function. The basic idea is to start with an approximate guess
for the zero, then use the formula below to turn that guess into
a better approximation. This process is repeated until, after
only a few steps, the approximation is extremely close to the actual
value of the zero.
Note: In some circumstances, Newton's
method backfires and gives successively worse and worse approximations.