Finding the fourth local extreme point and inflection points of a quintic polynomial constructed by three stationary points using symbolic formulas.
This applet is an addition to the earlier applets 1 and 2.
In the Michael Borcherds applet using three moving points P1, P2, P3, a quintic polynomial ff(x) is explicitly defined (using symbolic formulas).
In the present applet, also using symbolic formulas, the existing fourth local extremum P4 is determined, as well as 3 points of inflection -R1, R2, R3. The abscissas z1, z2, z3 of the inflection points, the three roots of the corresponding cubic polynomial ff''(x), are, as expected, real numbers.