Newton-Raphson method

The Newton-Raphson method, visualized below, finds roots of a function $f$ by:

1. Starting with an initial guess of the root $x_0$.
2. Defining $x_{n+1}=x_n-\frac{f(x_n)}{f^{\prime }(x_n)}$.
3. Iterating until $x_n$ is close to zero and/or the sequence of $x_n$ does not oscillate a lot.