# Find the Slope of a Curve with the TI-84 Plus

You can find the slope of a curve with the TI-84 Plus calculator, even though it is not equipped to find the derivative of a function. For example, it can't tell you that the derivative of *x*^{2} is 2*x**.* But the calculator is equipped with a numerical routine that evaluates the derivative at a specified value of *x**.*

This numerical value of the derivative is the slope of the tangent to the graph of the function at the specified *x*-value. It is also called the slope of the curve.

To find the slope (derivative) of a function at a specified value of *x*, perform the following steps:

Graph the function in a viewing window that contains the specified value of

*x*.To get a viewing window containing the specified value of

*x*, that value must be between**Xmin**and**Xmax**.Press [2nd][TRACE] to access the Calculate menu.

Press [6] to select the dy/dx option.

If necessary, repeatedly press the up- and down-arrow keys until the appropriate function appears in the border at the top of the screen.

This is illustrated in the first screen.

Enter the specified value of

*x*.To do so, use the keypad to enter the value of

*x**.*As you use the keypad,**X=**appears, replacing the coordinates of the cursor location appearing at the bottom of the screen in Step 4. The number you key in appears after**X=**. This is illustrated in the second screen. If you make a mistake when entering your number, press [CLEAR] and re-enter the number.If you are interested only in finding the slope of the function in a general area of the function instead of at a specific value of

*x*, instead of entering a value of*x*, just use the left-arrow key and the right-arrow key to move the cursor to the desired location on the graph of the function.Press [ENTER].

After pressing [ENTER], the slope (derivative) is displayed in the border at the bottom of the screen. This is illustrated in the third screen.