Main Window:

The upper half of the main window should look similar to following:

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The thick dark gray curve represents the selected function.  To change the function, select Function form the main menu.  The secant line is drawn from the intersection point of the vertical line labeled x and the curve to the intersection point of the vertical line labeled x+dx and the curve. The slider controls the position of the x line.  The distance dx can have three values: 0.1, 1.0 and 2.0.  Click on the desired dx distance to set it.  

The bottom half of the window contains a view similar to the one shown below:

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The thick dark gray line is a plot of the derivative of the function.  It is not displayed unless the Plot Derivative button is clicked.  The three other thin lines are user-created.  The thin black line is the approximated derivative with a dx of 0.1.  The dark gray line corresponds to a dx of 1.0 and the light gray line is for a dx of 2.0.  These lines are created using the Plot Point button.  

As the slider is moved, a small square filled with the color corresponding to the selected dx moves in the bottom view.  This is the approximated value of the derivative at that location.  The Plot Point button will record the position of the block.  If the slider is moved and Plot Point is selected again, a line segment will be drawn from the previous plotted point to the current one. The approximated curve will be smoother if more points are plotted.

Notice that the accuracy of the approximated derivative increases with decreasing values of dx.  

The Init button clears the bottom view.