E1: Choose a model point with the slider. Draw the red point to the blue model point (limiting process with vanishing difference).

The secant turns into a tangent, the magenta colored difference quotient becomes a point on the beige first derivative = a differential quotient.

E2: Move the model point near a maximum or minimum of the sine function and study the context.

E3: Position the model point close to the steepest point of the curve and study the process when you cross the inflexion point.

E4: Try several model points of the sine and convince yourself that the limiting process will always lead to a point on the cosine.

E5:  After this experience, how would you design an algorithm for the numerical calculation of the first derivative of an arbitrary, continuous function?

E6: How would you design an algorithm for the second derivative?