Exercises

In these exercises, plotting data refers to the critical points of a function, the local and global maxima and minima of the function, the inflection points of the functions. Remember, determining whether a critical point is a maximum or minimum or whether a point is an inflection point require algebraic tests.

1. Determine the plotting data for each of the following functions.
   1. .
   2. 
   3. .
2. Each of the following functions depends on a ``parameter'' a. For each value of a, the expression for f gives a different function of f. However, it makes sense that all the functions given by the expression are related, so We say that the formula represents a family of functions rather than a single function. In the calculations, the parameter should be treated as a constant. However, your answers will depend on the parameter. For each of the following, determine the plotting data and describe in words how the data depends on the parameter. In particular, if the parameter is made larger, how does this affect the data? if the parameter is made smaller, how does this affect the data?
   1. .
   2. .