Graphing derivatives
How to show the trace of an object
Objects can leave a trace in the
Graphics View when they are moved. There are two ways of showing the trace of an object:
Graphics View.
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- Select the object whose trace you would like to show. Use the
Style Bar button to open the
Settings. Check
Show Trace on tab Basic. OR
- Right-click (MacOS: Ctrl-click, tablet: long tap) an object and check
Show Trace in the appearing context menu.
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Task
Graph the derivative of a function by tracing the slope of point A.
Explore the construction...
Move point A so that the point S graphs the slope function.
Instructions
Re-create the construction above by following the steps listed below:
1. | ![]() | Enter the polynomial f(x) = x^2/2 + 1 . |
2. | ![]() | Create a new point A on function f. Hint: Point A can only be moved along the function. |
3. | ![]() | Create tangent g to function f through point A. |
4. | ![]() | Create the slope of tangent g using m = Slope(g) . |
5. | ![]() | Define point S = (x(A), m) .
Hint: x(A) gives you the x-coordinate of point A. |
6. | ![]() | Connect points A and S using a segment. |
7. | ![]() | Turn on the trace of point S and move point A. Hint: Right-click point S (MacOS: Ctrl-click, tablet: long tap) and select Show Trace. |
8. | ![]() | Close the ![]() ![]() |
9. | ![]() | Display the Input Bar using the ![]() |
Try it yourself...
Reuse your construction
Change the equation of the initial polynomial f(x) to produce a new problem. For example, enter
f(x)= 2 x²
into the Input Bar. You might want to zoom if point A lays outside of the visible area after changing the function.Learn more about the Trace feature
The
Show Trace feature has some special characteristics:
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- A trace is a temporary phenomenon. Whenever the graphics are refreshed, the trace disappears (e.g. on zoom). If you want to display a permanent trace of a point you can use the
Locus tool or command.
- The trace cannot be saved and is not shown in the
Algebra View.
- You can turn off the trace of an object by unchecking
Show Trace either in the
Settings or the context menu.
- The menu item Refresh Views in the
View menu clears all traces. Hint: If you are using GeoGebra Desktop or the Online or Tablet App, you can also use the key combination Ctrl – F to refresh the Views.