Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process.
Would this be a good explanation?
The process of global optimization refers to the task of finding the absolute set of parameters such as the minima or maxima points of the function within the given domain. When given an equation, the graph of the maximum and minimum points of the equation always has a slope of zero. Due to this fact, you must use the first derivative rule and take the first derivative of the equation and set it equal to zero. This will then give us every value or critical point at which the slope is zero, and will essentially tell us where the global max, global minimum, or neither points are on the graph. In order to identify what the critical points are, you can take the second derivative of the equation and set it equal to zero. The critical points where the line is concave down or increasing to decreasing are the global max. The critical points where the line is concave up or decreasing to increasing are the global minimum. If there is a critical point where the line does neither of these then the critical point is identified as neither.
Calculus - bobpursley, Monday, October 27, 2008 at 7:30pm
Exactly like my first calculus text read.