E1: Start with the default values : x1 = 0.5; delta=1
Compare how well the three procedures approximate the analytic solution.
E2: Draw the initial value with the mouse. Observe the shift of the analytic solution, and its relation to the result of the different algorithms. Explain mentally to some non professional what you observe!
E4: Reduce the interval width and observe how fast the approximations converge to the analytic solution.
E4: Keep the interval small and approximately constant while drawing the initial point. Observe whether the differences of the algorithms are comparable for all initial points. Interpret the result!
E5: For special initial points the simple algorithms result in exact agreement with the analytic value, while the parabola algorithms shows a recognizable deviation. Does this mean that the simple ones are better? What is the reason for identity in these cases?