### Introduction

The calculation of the optimum value of a function of two variables is a common requirement in many areas of engineering, for example in thermodynamics. Unlike the case of a function of one variable we have to use more complicated criteria to distinguish between the various types of stationary point.

#### Prerequisites

• understand the idea of a function of two variables
• be able to work out partial derivatives

#### Learning Outcomes

• identify local maximum points, local minimum points and saddle points on the surface $z=f\left(x,y\right)$
• use first partial derivatives to locate the stationary points of a function $f\left(x,y\right)$
• use second partial derivatives to determine the nature of a stationary point