In this lesson, our instructor Vincent Selhorst-Jones teaches how to find points of interest on a graph. Hell show you some interesting points on a graph, go over roots/zeros, relative minimums, relative maximums, and intersections. Youll go through the process of finding points of interest and then learn two advanced techniques: arbitrary solving and calculus. Youll even find out how to show you work even though you used a calculator.
We often want to find the "interesting" points on a graph: places where something special occurs. A graphing calculator will allow us to easily find these locations. You can use a graphing calculator to find things like
Roots/Zeros (zero): locations where f(x) = 0;
Relative Minimums (min): lowest (local) values;
Relative Maximums (max): highest (local) values;
Intersections (intersection): location where two functions intersect each other.
The specific menu to get access to these varies from one calculator to another, but the menu choices should look something like those above. Set up your function, then choose whichever one you want.
For most points of interest, you begin by graphing the function, choosing which type of point you're interested in, then telling the calculator where to search. It searches that portion for the point you're interested in, then gives you the value.
The problem with using a calculator to find these "interesting" points is that the calculator does all the work for you. While that's okay in some situations, you still should be able to work out solutions for problems like this on your own. Don't become
dependent on your calculator for all your solving. You can use it as a way to check your work or solve a problem you can't do algebraically, but don't let it become a crutch that replaces thinking.
Finding Points of Interest
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.