Find a polynomial function of degree 3 having a stationary inflection point at [i](1, 1)[/i] and passing through point [i](2, 2)[/i].

[table][tr][td]1.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/4/47/Menu_view_cas.svg/20px-Menu_view_cas.svg.png[/img][/td][td]In the [i]Input Bar[/i], define the function [code]f(x):= a x^3 + b x^2 + c x + d[/code].[/td][/tr][tr][td]2.[/td][td] [code]p[/code][/td][td]According to the task, the function value at [i]x=1[/i] is 1. Enter [code]p: f(1) = 1[/code];[br] and press the Enter key.[br][b]Hints:[/b] The input ":" names your equation, while the semicolon “;” suppresses the output.[/td][/tr][tr][td]3.[/td][td] [code]q[/code][/td][td]We also know that the function value at [i]x=2[/i] is 2. Enter [code]q: f(2) = 2[/code][code];[br][/code]into the [i]Input Bar[/i].[br][/td][/tr][tr][td]4.[/td][td] [code]r[/code][/td][td]Since (1, 1) is an inflection point, the first derivative equals 0 at [i]x=1[/i]. Enter [code]r: f'(1) = 0[/code][code];[br][/code][b]Hint:[/b] The derivative of[i] f[/i] can be written as f'.[/td][/tr][tr][td]5.[/td][td][code] s[/code][/td][td]We also know that the second derivative equals 0 at [i]x=1[/i]. Enter [code]s:[/code][code] f''(1) = 0;[br][/code][/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_solve.png[/icon][/td][td]Select rows two through five and apply the [i]Solve [/i]tool.[/td][/tr][tr][td][/td][td][/td][td][b]Hints: [/b][br][list][*]Press and hold the [i]Ctrl[/i]-key while clicking onto the corresponding row numbers to select several rows at the same time.[br][/*][*]You can achieve the very same by using the [i]Solve [/i]command instead:[br][code][/code][code]Solve({p, q, r, s}, {a, b, c, d})[br][/code][br][/*][/list][/td][/tr][tr][td]7.[/td][td][code]Substitute[/code][/td][td]Enter [code][/code][code]Substitute($1, $6)[/code] into the [i]Input Bar[/i] and press the [i]Enter [/i]key. [br][b]Note:[/b] You just substituted the undefined variables in the formula of [i]f[/i] ([code]$1[/code]) with the solutions you just calculated ([code]$6[/code]). [/td][/tr][tr][td]8.[/td][td][img]https://wiki.geogebra.org/uploads/thumb/3/34/Algebra_hidden.svg/32px-Algebra_hidden.svg.png[/img][/td][td]Activate the disabled [i]Visibility [/i]button below row number 7 to plot the function in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i].[/td][/tr][/table]