In this weeks’ comparison of the Casio vs. TI calculators, I demonstrate how to find a max/min of a given function, using the Casio Prizm and the TI-84+ CE. In my example I use a cubic function because it allowed me to show both a maximum point and a minimum point on the curve. Why might students be asked to find a max/min point of a function you ask? Well, besides the obvious ‘on a standardized test’ question, what we really want students to be able to do and understand is what the max/min points mean in the context of the problem/situation. In a real-world application, how does that max/min point help us understand what is going on in the problem? The short answer is it provides specific points where ‘something’ has happened, and finding these points provides insight, allowing students to ask different questions or analyze the situation.
Here is a common example: A quadratic function might be used to model the path of a ball as it is thrown or hit, with x representing time and y representing its’ height. So the max point in this case would be the maximum height of the ball at a given point in time before it begins its descent back to earth. We want students to be able to find that max/min point, in context, so they can answer questions or make conjectures about the ball. For instance, in this ball example, is it possible to change the angle the ball is thrown/hit to increase the max height, but keep the time the same? Being able to quickly find these max/min points so that interesting questions and conjectures can be made and students can apply mathematics in challenging and deeper ways is one benefit of using technology, such as graphing calculators. The max/min points can be a starting point for deeper exploration.
Below is a quick video on how to find a max/min point of a function (using a cubic as the example, since it has an example of both a maximum and minimum point).