Applications of the Derivative
                                                   Integration
                         Calculus: Applications and Integration
                     POLI 270 - Mathematical and Statistical Foundations
                                                Sebastian M. Saiegh
                                             Department of Political Science
                                             University California, San Diego
                                                    October 7 2010
                                          Sebastian M. Saiegh      Calculus: Applications and Integration
                                  Applications of the Derivative
                                                   Integration
     Calculus: Applications and Integration
           1   Applications of the Derivative
                   Mean Value Theorems
                   Monotone Functions
           2   Integration
                   Antidifferentiation: The Indefinite Integral
                   Definite Integrals
                                          Sebastian M. Saiegh      Calculus: Applications and Integration
                                     Applications of the Derivative      Mean Value Theorems
                                                        Integration      Monotone Functions
      Introduction
           Last week, we looked at the idea of instantaneous rate of change,
           and we learned how to find the derivative of a function.
                    Today, we are going to focus on some applications of the
                    concept of the derivative.
                    In particular, we will find out how to use derivatives to locate
                    the intervals in which a function is monotone and those points
                    in the domain where a graph of a function presents some
                    special characteristics.
           These notions are critical for the study of optimization problems in
           political science.
                                              Sebastian M. Saiegh        Calculus: Applications and Integration
                                     Applications of the Derivative      Mean Value Theorems
                                                        Integration      Monotone Functions
      Calculus: Applications and Integration
           1    Applications of the Derivative
                     Mean Value Theorems
                     Monotone Functions
           2    Integration
                     Antidifferentiation: The Indefinite Integral
                     Definite Integrals
                                              Sebastian M. Saiegh        Calculus: Applications and Integration