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