Example 2: Using the Calculator

Given $f\left(x\right)=3x^2–9x+13$, find $f\prime \left(3\right)$.

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 , .

Final Result:

The value of the derivative, $\frac{\mathit{dy}}{\mathit{dx}}$, of the function $y=3x^2–9x+13$ at x = 3 is 9 .

Meaning:

–           The instantaneous rate of change of $y=3x^2–9x+13$ at x = 3 is 9 .

–           The slope of $y=3x^2–9x+13$at x = 3 is 9 .

The slope of the tangent line to $y=3x^2–9x+13$ at x = 3 is 9 .