Mathematics for Electrical Engineering and Computing

11

Maxima and minima and sketching functions

11.1 Introduction

Differentiation can be used to examine the behaviour of a function and find regions where it is increasing or decreasing, and where it has maximum and minimum values. For instance, we may be interested in finding the maximum height, maximum power, or generating the maximum profit, or in finding ways to use the minimum amount of energy or minimum use of materials. Maximum and minimum points can also help in the process of sketching a function.

11.2 Stationary points, local maxima and minima

Example 11.1

Throw a stone in the air and initially it will have a positive velocity as the height, s, increases; that is, ds / dt > 0. At some point it will start to fall back to the ground, the distance ...