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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 x2 is 2x. 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:

  1. 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.

  2. Press [2nd][TRACE] to access the Calculate menu.

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

  4. 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.

  5. 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.

  6. 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.

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