# Chapter 10: Higher Derivatives, Taylor Series, Quadratic Approximations and Accuracy of Approximations

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## Introduction

We investigate quadratic and higher polynomial approximations to a function culminating in the Taylor series. Application to behavior at critical points and to determining the accuracy of approximations are discussed.

## Topics

10.1 The Quadratic Approximation

10.2 Higher Approximations and Taylor Series

10.3 Uses of Higher Approximations

10.4 Quadratic Behavior at Critical Points

10.5 Accuracy of Approximations, and the Mean Value Theorem