4.3 Global Maxima and Minima

Main Points:
Global Maxima occure at the greatest value for a function not constrained by a certain interval (except by the endpoints of the function if it has endpoints). Global Minima occure at the lowest value for a function not constrained by a certain interval. To find the global maxima or minima, compare all critical points of the function as well as the endpoints. If the function continues to infinite or -infinite, then there is no global maxima or minima respectively.

Challenges:
When I looked at the gas consumption example in the book, and I saw the graph, my first reaction was, "hey 20 mph must be most efficient since they're talking about global maxima and minima, but I quickley realised the problem is slightly more complicated. They were looking for most efficient mpg's not gallons per hour, the book made a good point that maximizing or minimizing a function definately goes beyond finding the highest point on a graph.

Reflections:
I think this will help more so than just a local max or min in solving real world problems that require maximizing or minimizing something. I could be wrong, but this concept seems to be more applicable in more realistic problem solving.