Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 6 / d

The tangent line to $f$ at $x_n$ is $y=f(x_n)+f^{\prime }(x_n)(x-x_n)$. Its intersection with the horizontal axis gives Newton's method:Each step requires $f^{\prime }(x_n)\ne 0$. Convergence to a zero of a function additionally depends on the starting point and the local behavior of $f$; the update formula alone is not a convergence guarantee.