# rootfinding

1. ### Deriving Newton's root-finding method with Taylor polynomials.

Hi, when deriving Newton's method using Taylor polynomials my book considers the first Taylor polynomial expanded about \overline{x} where \overline{x} is an approximation to the root p such that f'(\overline{x})\neq 0 and |p-\overline{x}| is small. f(x) = f(\overline{x}) +...
2. ### Rootfinding

To help determine the roots of x = tan(x), y = x, and y = tan(x), and look at the intersection points of the two curves, find the smallest nonzero positive root of x = tan(x) with an accuracy of ε=0.0001, where ε is the error tolerance. The desired root is > than pi/2