Unconstrained optimization in 1-d and 2-d

Chapter 4.3


1) Main Points

Chapter for 4.3 deals with global maxima and minima, where the function is larger or smaller than anywhere else in the function. On an interval that includes end points to find the global max/min you compare the values of the function at all critical points. If a function has no real end points then there are no global maxima or minima because the function is continuous. Maxima and minima occur on either a critical point or an end point, they can occur nowhere else. If you plug in the x values of the critical points and the end points the highest and lowest numbers are the end points.

2) Challenges

The hardest part of finding the global maxima/minima is being able to find the critical points. I am confused why in example two they used a second derivative to find the critical points. Another thing to remember is that once you find the x values of the critical points you plug those back into the original function NOT the function of the derivative to find which is max or min.

3) Reflections

Global maxima and minima seem like they will be most useful in determining real world problems in which you are looking for a maximum or a minimal value. For example when you are looking for the maximum profit you want the global maximum instead of just the local.