Part 1 PARTIAL DERIVATIVESMAT 295 103 Chapter 8 Extremum of Functions At the end of this cha pter, students shou ld be able to: Define, compute and classify critical points for a function of two variables Define and compute the relative extrema for a function of two variables Solve applied extrema problems 8.1 Introduction In earlier chapter the discussion involved application of partial derivatives. In chapter 7, problems such as determining the slope of the tangent line at a point ) , ( b a and rate at which a volume of certain object change as the dimension changed were look into. In chapter 8, another application of partial derivatives will be explored. Refer to Figure 8.1, the graph consist of high and low points. Among the higher and lower points, it is possible to have the highest and lowest point among all points. What are these points and how can they be located? To answer this question an understanding of the critical point and the extremum for a function of a single variable is required.