Differentiation

Introduction

A function f(x) is differentiable at the point x0 if ∃ f' such that for all ε > 0 sufficiently small, there exists a δ > 0 such that ∀ x with | x - x0 | < δ then

| ((f(x) - f(x0)) / (x - x0)) - f' | < ε

The value of f' is called the derivative of f at the point x0.