[size=85] This applet is an addition to the earlier applets [url=https://www.geogebra.org/m/jc3hpzrd]1[/url] and [url=https://www.geogebra.org/m/c5trvgmv]2[/url].[br]In the Michael Borcherds [url=https://www.geogebra.org/m/jc3hpzrd]applet[/url] using three moving points [b][color=#1e84cc]P1[/color][/b], [b][color=#1e84cc]P2[/color][/b], [b][color=#1e84cc]P3[/color][/b], a quintic polynomial [b][color=#38761d]ff(x)[/color][/b] is [i][u]explicitly[/u][/i] defined (using symbolic formulas).[br] In the present applet, also using symbolic formulas, the existing fourth local extremum [b]P4[/b] is determined, as well as 3 points of inflection -[color=#9900ff][b]R1[/b], [/color][b][color=#9900ff]R2[/color][/b], [b][color=#9900ff]R3[/color][/b]. The abscissas [b][color=#9900ff]z1[/color][/b], [b][color=#9900ff]z2[/color][/b], [b][color=#9900ff]z3[/color][/b] of the inflection points, the three roots of the corresponding cubic polynomial [b][color=#9900ff]ff''(x)[/color][/b], are, as expected, [i]real[/i] numbers.[/size]