How to Draw Tangent Lines on a TI-84 Graphing Calculator

Tangent lines are lines that intersect a curve at a single point and are parallel to the curve’s slope at that point. They are useful for analyzing the behavior of a function at a specific point.

Materials

• TI-84 graphing calculator
• Graph of the function

Steps

1. Enter the function into the graphing calculator. Use the “Y=” menu to enter the function. For example, to graph the function y = x^2, press the “Y=” button, then enter “x^2”.
2. Graph the function. Press the “GRAPH” button to graph the function.
3. Move the cursor to the point where you want to draw the tangent line. Use the arrow keys to move the cursor to the desired point.
4. Press the “TRACE” button. This will open the trace menu.
5. Select the “Tangent” option. This will calculate the slope of the function at the selected point and draw a tangent line.

Additional Features

• Tangent Line Calculator: You can use the TI-84’s tangent line calculator to find the equation of the tangent line. To access the calculator, press the “CALC” button, then select “4:Tangent”.
• Derivative: The TI-84 can also calculate the derivative of a function, which can be used to find the slope of the tangent line at any point. To calculate the derivative, press the “2nd” button, then the “DERIV” button.

Tips

• If the function is not smooth at the selected point, the tangent line may not be accurate.
• You can use the zoom feature to zoom in on the point where you want to draw the tangent line. This will make it easier to position the cursor accurately.
• You can also use the “FnLink” feature to connect two TI-84 calculators and share data. This can be useful if you want to draw tangent lines on a graph that is stored on another calculator.

Applications

Tangent lines are used in a variety of applications, including:

• Optimization: Tangent lines can be used to find the maximum or minimum value of a function.
• Curve Fitting: Tangent lines can be used to approximate the behavior of a function over a small interval.
• Rate of Change: Tangent lines can be used to find the rate of change of a function at a specific point.

Common Mistakes to Avoid

• Selecting the wrong point: Make sure to select the point where you want to draw the tangent line accurately.
• Not zooming in: If the function is not smooth at the selected point, zooming in can help to improve the accuracy of the tangent line.
• Using the wrong calculation: The TI-84 has several different calculators that can be used to find the tangent line. Make sure to select the correct calculator for the task.

Pros and Cons

Pros:

• Easy to use
• Can be used to find the equation of the tangent line
• Can be used to calculate the derivative of a function

Cons:

• May not be accurate if the function is not smooth at the selected point
• Can be difficult to use on complex graphs

Conclusion

Tangent lines are a powerful tool for analyzing the behavior of functions. The TI-84 graphing calculator provides several easy-to-use features for drawing tangent lines. By following the steps outlined in this article, you can quickly and accurately draw tangent lines on any graph.