|Open a new GeoGebra
worksheet. Enter the function f(x) = cos(3x) / (1 + x^2) .
Make the graph blue and a little thicker.
Next, type f '(x) into the input bar. GeoGebra automatically calculates the derivative of f(x).
Select the New Point tool and click anywhere on the graph of f . Color the point red.
Select the Tangent Line tool then click on the point and the function f . Make the tangent line dashed.
|Select the Slope tool and click the line. In the
Algebra View, click the circle next to m to hide the slope.
Select the Text tool and enter
"Slope of tangent: " + m
Increase the size of the text, if you wish.
Hide the graph of f '(x).
In the Input Bar, type ( x(A), m ). This creates a point B whose x-coordinate is the x-coordinate of A (the red point on f) and whose y-coordinate is m. As we drag point A, point B follows the derivative curve. Make B green.
Right-click point B and select "Trace On". Now, as A is dragged, B leaves a record of its path. You can hide/unhide the graph of f '(x) to confirm that this really is the graph of the derivative.
|Turn off tracing on B, and from
the View menu, choose Refresh Views to remove the trace of
Hide everything except for f and f '.
To copy the entire Graphics View to the clipboard, choose the menu Edit > Graphics View to Clipboard. Then you can paste the picture into another program.
Often it's useful to capture only a portion of the Graphics View. If you click and drag a rectangle first, then only the portion of the Graphics View in the rectangle gets copied to the clipboard. For instance, I might copy the view on the right and put it into a quiz where I ask students to identify which graph is f and which is f '.
|Finally, suppose you want to use
this worksheet as part of a classroom presentation. You can
increase the size of the screen elements by selecting Options > Font Size. Now
the people in the back of the classroom can see what you're doing!