Unconstrained Optimization in 1-d and 2-d (10/21/2008)

1. Main Points

The main point of today’s reading was to learn about how to determine global maxima and minima of functions. To find the global maximum and minimum of a continuous function on an interval including endpoints, one compares values of the function at all the critical points in the interval and at the endpoints. When excluding endpoints, one finds the values of the function at all the critical points and sketches a graph.

2. Challenging

I see that they use differentiation, then setting equal to zero and then solving for x in the examples. I do not remember well the tactics used for factoring out when solving for zero, maybe you can go over this quick in class?

3. Intriguing

I realize that being able to maximize and minimize when solving different problems in all natural and social sciences must be very useful. I particularly found the example showing what speed to drive in order to have the smallest gas consumption interesting and very useful. I will drive at about 50 mph as much as I can from now on!