Maxima and minima pop up all over the place in our daily lives. They can be found anywhere we are interested in the highest and/or lowest value of a given system; if you look hard enough, you can probably find them just about anywhere! Here are just a few examples of where you might encounter maxima and minima:

* A meteorologist creates a model that predicts temperature variance with respect to time. The absolute maximum and minimum of this function over any 24-hour period are the forecasted high and low temperatures, as later reported on The Weather Channel or the evening news.

* The director of a theme park works with a model of total revenue as a function of admission price. The location of the absolute maximum of this function represents the ideal admission price (i.e., the one that will generate the most revenue).

* An actuary works with functions that represent the probability of various negative events occuring. The local minima of these functions correspond to lucrative markets for his/her insurance company – low-risk, high-reward ventures.

* A NASA engineer working on the next generation space shuttle studies a function that computes the pressure acting on the shuttle at a given altitude. The absolute maximum of this function represents the pressure that the shuttle must be designed to sustain.

* A conscientious consumer meticulously collects data on his/her cell phone usage over a certain interval (say, a month) and develops a function to represent cell phone usage over time. The local maxima and minima of this function give the consumer a better idea of his/her usage patterns, empowering him/her to choose the most appropriate cell phone plan.