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

Find approx. solutions to $f(x) = 0$

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

Initial guess for the root

Tangent line

$|x_{n+1} - x_n| < \epsilon$

When initial guess is close to actual root

When $f'(x)$ is close to zero

Flat slope or discontinuity

May converge to different roots depending on $x_0$

Good initial guess