Newton's method

Newton's method is an iterative algorithm to find a solution to $f(x) = 0$ given an initial guess $x_0$. The update step is $x_{n+1} = x_n - f(x_n)/f'(x_n)$. The graphic below shows the graph of $f(x)$ and traces the algorithm using the geometric interpretation that $x_{n+1}$ is the intersection point of the tangent line to $f(x)$ at $x_n$ with the $x$ axis.

$x_0 =$

0.9