You see here the function f(x) = x²/6 - 2x + 8 and its tangent line t together with a slope triangle. The slope s of the tangent line is drawn again starting at the x-axis.

1) Drag point T with the mouse. This produces a trace of the slope creating the graph of the slope function.
Which kind of function is this slope function? Try to find the slope function's equation, too. Write down all your results.
2) Calculate the first derivative of the function f on paper.
3) Double click on the drawing pad, type the first derivative of f into the input field and press Enter.
Choose the "move mode" and drag point T with your mouse again. What is happening? Write down your observations.