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:

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.

Then, modify the construction so that the object, whose trace you turned on, changes its position and leaves a trace in the

Graphics View.

Graph the derivative of a function

by tracing the slope of point A.

Move point A so that the point S graphs the slope function.

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 Algebra View by unchecking the corresponding option in the View Menu.
9.		Display the Input Bar using the View Menu.

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.

The

Show Trace feature has some special characteristics:

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.