4.3: Global Maxima and Minima/ 9.5: Critical Points and Optimization

Main Points
Local maxima and minima deal with where a function has greater or smaller values at surrounding points; global maxima and minima deal with the largest and smallest values respectively. In order to find the global maxima and minima one would need to find and graph all the critical points.
In finding the greatest or smallest value of a function is to optimize it.

Challenges
I do not understand how to use the analytical method of finding the local maximum or minimum for more than one variable. I might understand the second derivative test equivalent for this too if I understood how it was done (the analytical method that is).

Reflections
Global extrema seems to me to be a lot more useful than local extrema, in which case I find it difficult to udnerstand the great significance of the local extrema. Global extrema helps you find the "extreme" max or min of any function. This is a lot more useful I would think.