The document discusses numerical methods for estimating the derivative of a function f(x) at a point x=xi. It introduces three approaches: 1) the forward difference approximation calculates the slope between xi and xi+h, 2) the backward difference approximation calculates the slope between xi-h and xi, and 3) the centered difference approximation calculates the average of the forward and backward slopes. Each method has an error term that approaches zero as h approaches zero.