Title: 12_2 Maxima and Minima
Course: HELM Workbooks 2023-2024 > Section: HELM 12: Applications of Differentiation

In this Section we analyse curves in the ‘local neighbourhood’ of a stationary point and, from this analysis, deduce necessary conditions satisfied by local maxima and local minima. Locating the maxima and minima of a function is an important task which arises often in applications of mathematics to problems in engineering and science. It is a task which can often be carried out using only a knowledge of the derivatives of the function concerned. The problem breaks into two parts

- finding the stationary points of the given functions
- distinguishing whether these stationary points are maxima, minima or, exceptionally, points of inflection.

This Section ends with maximum and minimum problems from engineering contexts.