Method 2: Using the Calculator

While the calculator will not calculate a derivative equation, it will evaluate a derivative at a specific value. Since you will have a calculator allowed sections on the AP Calculus Exam, and often on your in-class tests, I wanted to provide you a method you can use on your calculator to evaluate a derivative at a single value.

There are two places on your calculator that you can evaluate a derivative. I will show you how to do it using the graphing section of your calculator. I do this because older versions of TI-83/84’s don’t have the other option, and because it is often times helpful to see the actual graph of your equation.

Step 1: Plug your original equation, $f\left(x\right)$, into Y1 on your calculator.

Hit the Y= button, , in the top left corner of the calculator, and then enter you equation into Y1, , there.

Step 2: Graph the equation.

Hit the graph button, , in the top right corner of the calculator.

Step 3: Select the $\frac{\mathit{dy}}{\mathit{dx}}$ option from the Calc menu on the calculator.

You will find this option by hitting 2 ^nd , , then select the Calc menu (button above Trace at the top of the calculator, , and then choose the #6 $\frac{\mathit{dy}}{\mathit{dx}}$ option, .

Step 4: Enter the x-value you are wanting to evaluate the derivative at, and then hit the Enter button.

At the bottom of the screen, you will be asked to input the x-value that you want to evaluate the derivative at. Type in that value, , and hit Enter, .

IMPORTANT:

• The calculator will not prompt you to enter the x-value . You will just need to know that this is how the process works on the calculator.
• Make sure your x-window is large enough to take in the x-value you are typing in. The standard window on the calculator is set with an x-minimum of -10 and an x-maximum of 10. If you need to evaluate x=23 , then you will need to extend that x-maximum to be larger than 23 .

Step 5: Read the answer at the bottom of the calculator screen.

If you did everything right, then at the bottom of your calculator screen you will see $\frac{\mathit{dy}}{\mathit{dx}}$= Your Answer , .