I am using a TI-84 Plus Silver Edition graphing calculator for demonstrations; consult your calculator's manual for help finding menus and buttons.
In the previous post, we learned how to use the value, zero, minimum, and maximum commands found in the Calculate menu on a graphing calculator (click here to view that post). Today, we will look at the last three commands: intersect, derivative, and integral. In an Algebra class, you will probably use the intersection command frequently, but you will not use the derivative and integral commands until you reach Calculus. Even then, many students do not realize the advantage those two little commands offer. Let's get started.
To begin, refer to the first set of instructions in the previous post linked above to set up your calculator with our function and window, so that you can see the graph I'll be working with throughout this post.
HOW TO USE THE "INTERSECT" COMMAND
The "intersect" command allows you to determine the point of intersection of two functions. For this section, input the following function into the second slot in the Y= menu.
The "intersect" command is also helpful for finding all x-values that yield a particular y-value. For example, if we want to know at what points our first function is equal to -10, we can do the following:
Change the second function to y = -10.
HOW TO USE THE "DERIVATIVE" COMMAND
Clear the second function from your calculator, but keep the first one and graph it in the same window we've been using. The "derivative" command allows you to determine the derivative of the function at any given x-value in the window you have set. Open the Calculate menu and choose option 6: dy/dx. You can choose an x-value in one of two ways: move the cursor along the curve to the point you desire or type in the x-value you want to evaluate. Let's evaluate the derivative at x = 5. When you type a number, an input line will appear automatically.
HOW TO USE THE "INTEGRAL" COMMAND
I cannot input the "integral" symbol here, but the final Calculate command is the integral. The integral over an interval is the area under the curve (between the curve and the x-axis) over that interval. To practice, let's find the integral of this function over the interval (1, 5). With the same function graphed on your screen, open the Calculate menu and choose the last option. The calculator will place a cursor on the screen (circled in blue below) and opens with the first prompt (circled in red below): "Lower Limit?"
There you have it. We have now covered all of the commands found in the Calculate menu. I hope you now have the ability and confidence to use these commands to help you perform well in your math classes. Most math teachers/professors require you to show your steps on homework, but these commands allow you to very easily check your answers before turning in your work. If you have any questions or comments, please leave them below!