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.
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