Graph the derivative of a function. [br][br]Watch the video below and learn how to create an applet for exploring the derivative with [i][url=https://www.geogebra.org/graphing]GeoGebra Graphing Calculator[/url][/i]. Then try it yourself by following the instructions below.

[table][tr][td]1.[/td][td][/td][td]Enter [math]f(x)=-0.25(x-1)(x+1)(x+3)[/math] into the [i]Input Bar[/i].[/td][/tr][tr][td]2.[/td][td][/td][td]Create a slider for a parameter [i]n[/i]. Therefore enter [math]n[/math] into the [i]Input [/i][i]Bar[/i] and press [i]Enter. [/i]A slider for[i] n [/i]will be created automatically.[br][/td][/tr][tr][td]3.[/td][td][/td][td]Create a point [i]A[/i] by entering the coordinates [math](n,f(n))[/math] into the [i]Input [/i][i]Bar[/i].[/td][/tr][tr][td]4.[/td][td][/td][td]Move the slider and explore how [i]A[/i] is moving along the graph of [i]f(x)[/i].[/td][/tr][tr][td]5.[/td][td][/td][td]Select point [i]A[/i] and change its point size and color.[/td][/tr][tr][td]6.[/td][td][/td][td]Enter the command [math]Tangent(A,f)[/math] into the [i]Input [/i][i]Bar [/i]to create a tangent [i]g[/i].[/td][/tr][tr][td]7.[/td][td][/td][td]Enter the command [math]Slope(g)[/math] into the [i]Input [/i][i]Bar[/i].[/td][/tr][tr][td][/td][td][/td][td][b]Note: [/b]The slope of the tangent [i]g[/i] will be labeled [i]a[/i] and displayed in the [i]Graphics View[/i].[/td][/tr][tr][td]8.[/td][td][/td][td]Again move the slider and watch how the tangent and slope are changing.[br][/td][/tr][/table]

[table][tr][td]9.[/td][td][/td][td]Create a point [i]B[/i] by entering the coordinates [math](n,a)[/math] into the [i]Input [/i][i]Bar[/i].[/td][/tr][tr][td]10.[/td][td][/td][td]Select point [i]B[/i] and change its color and point size.[/td][/tr][tr][td]11.[/td][td][/td][td]Move the slider and explore how point [i]B[/i] is moving.[/td][/tr][tr][td]12.[/td][td][/td][td]Enter [math]f'\left(x\right)[/math] into the [i]Input [/i][i]Bar [/i]to graph the derivative of [i]f(x)[/i].[br][/td][/tr][tr][td]13.[/td][td][/td][td]Move the slider again and explore how the graph of the derivative is retraced by point [i]B[/i].[/td][/tr][/table][br][b]Note: [/b]You can also open the context menu by pressing the [i]More [/i]button of point [i]B[/i]'s [i]Style Bar[/i] and activate [i]Show trace[/i]. When moving the slider, the [i]Trace [/i]of point [i]B [/i]is displayed and the graph of the derivative is retraced by point [i]B[/i]. The [i]Trace[/i] will be removed again when moving the [i]Graphics View[/i].