ABSTRACT
This chapter discusses the topics include limit theorems, differentiation, criterion for concavity and related theorems, and vector-valued functions. An application of the study of global and local extrema of a function leads to certain optimization problems. Recall that an optimal solution corresponds to the point or points where a given function attains an absolute maximum or absolute minimum value. Certain useful guidelines to solve such optimization problems are as follows: (i) Relative to a given problem, define a function to be optimized, then plot its graph and label the relevant quantities, if possible; (ii) label the quantity that needs to be optimized, and signify the appropriate domain, also known as the feasible domain, for the problem; and (iii) using the methods of §2.3, solve the problem. In economics, an isocost line represents the different combinations of two inputs or factors of production that can be purchased with a given sum of money.
