Math 105-02: Calculus I: Reading Homework 5.1

1. Using First and Second Derivatives : what are the connections between a function and its derivatives? why are these more useful now than in chapter 2? how are derivatives used in example 1?
   
   1. Local Maxima and Minima : what are local maxima and minima?
      
      1. critical points : what is a critical point? what is a critical value of a function? what is the relationship between critical points and local extrema (maxima or minima)?
         
      2. the first-derivative test : what is the first derivative test?
         
      3. the second derivative test : what is the second derivative test? how is it related to concavity? under what circumstances does it tell us nothing?
         
   2. Inflection Points : what is an inflection point? how might we locate one?
      
      1. inflection points and the derivative : what is the relationship between an inflection point of a function and the behavior of the first derivative of the function at that point?