Find f(x) = 0 Bisection method https://fr.wikipedia.org/wiki/M%C3%A9thode_de_dichotomie Newton method https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Newton We start at point $x_0$ (as close as possible to the solution). From Taylor 1st order: $$f'(x_0) \simeq \frac{f(x) - f(x_0)}{x-x_0}$$ We want to find $x$ such as $f(x)=0$ $$0= f(x_0) + f'(x_0)(x-x_0)$$ thus: $$x_{k+1} = x_k - \frac{f(x_k)}{f'(x_k)}$$