From Secant lines to Tangent lines

The derivative is defined as a limit of slopes of secant lines. As you look at the slope of the line passing through two points on the graph of a function, then let one of the points get closer and closer to the other, you should see that the slopes get closer and closer to the slope of the tangent line.
 
 







Instructions:

Adding Functions

Press "Add Function" button and type in a formula to be graphed in standard mathematical notation (eg "e^(-x/10)sin(x)"). The only variable the formula can use is x. You can add as many functions as you like, and "Delete Function" deletes the last one you entered.
Rescaling
This brings up a panel which you can use to edit the scale of the graph. The x variable runs between xMin and xMax, and the y values run between yMin and yMax. Use xScale and yScale to set the spacing of tick marks on the axes. If xScale or yScale is zero, the graph will have no tickmarks on that axis.
Zooming
You can change the scale of your picture quickly with "Zoom In", "Zoom Out" and "Zoom to Box". The first two zoom in or out around the center of the graph. If you click and drag on the graphing window, you can draw out a box, and Zoom To Box will zoom in to make that box fill the whole window.


Secant Lines

Click on the curve to mark a point on the curve. Click on a second point on the curve and another point is also selected, and you see the straight line (secant line) joining them. As you drag either one, the line and its slope change. If you select the ceheckbox to show the slope, the slope of the line is displayed on the screen as the nodes move. If you want to delete one or both nodes, draw out a box on the screen (as though you were going to zoom in) that encloses the nodes you want to delete, and then press the "backspace" key.



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Calculus on line home page

This utility provided courtesy of John Orr, Dept of Mathematics, University of Nebraska, Lincoln.




calonline:1398
Updated: 8/24/99