Slope Plotter
The user inputs a function f(x) in the box. The red point has coordinates (t, f(t)), where t is the current value of the slider. The slider moves across the interval [-10, 10] in increments of 0.4 units initially, but the user can change the lower bound, upper bound, and increment for the slider in the labeled boxes. [To move the slider or enter stuff in boxes you will need to select the pointer tool, the leftmost button on the toolbar.]
The dotted red segment is tangent to the graph y=f(x) at the red point, and its current slope is given as m (also in red) on the left side.
The large blue point has the same x-coordinate as the red point, but its y-coordinate is the slope m of the red tangent line. Dragging the slider moves both the red and bluepoints. The "Toggle Derivative Trace" checkbox allows the user to cause the position of the blue point to be traced in green as the slider is moved. [Traces can be erased by using the Move Graphics View button on the far right of the toolbar, and then clicking and slightly moving anywhere in the graphics window.]
Can you guess a "slope function" that goes through all the green points you've generated?
Put in any function you like, and generate a trace of the slope of the line at every point hit by the slider. Try to guess a function that passes through all of the green points you've generated.