Newton-Raphson (Edexcel A-Level Mathematics): Flashcards

Finding approximate solutions to equations $f(x) = 0$.

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

$f(x)$ is the function; $f'(x)$ is its derivative.

An initial guess $x_0$ for the root.

Ensure $|x_{n+1} - x_n| < \varepsilon$ for desired tolerance.

Choose an initial approximation for the solution.

The method may fail or converge slowly.

It may converge to the wrong root or fail to converge.

The method may converge to different roots based on $x_0$.

Graphically or analytically assess the function.