Graph the derivative of a function to observe the monotonicity. [br][br]Explore the construction and learn how to create an applet for exploring the monotony with respect to the derivative of a function 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]Enter [math]f'\left(x\right)[/math] into the [i]Input Bar[/i] to graph the derivative of [i]f(x).[/i][br][/td][/tr][tr][td]3.[/td][td][/td][td]Use the command [math]Extremum\left(f\right)[/math] to show the coordinates of the extrema of [i]f(x) [/i]as well as to display the points in the [i]Graphics View.[/i][/td][/tr][tr][td]4.[/td][td][/td][td]Enter [math]f'\left(x\right)>0[/math] to color the area for which the derivative of [i]f(x) [/i]is positive.[/td][/tr][tr][td]5.[/td][td][/td][td]Enter [math]f'\left(x\right)<0[/math] to color the area for which the derivative of [i]f(x) [/i]is negative.[/td][/tr][tr][td]6.[/td][td][img width=22,height=22]https://lh6.googleusercontent.com/kshG4DFPxWIrDos4CEJpfTNhmEmCMse2MiF1B7BDGX3tdHngKqjm34OLvEizE-6dMatwGnrP-BjvBMNorsDBzgKR3jDMvlmsoTZeSnEHVSjMHYPSILd3pzJgI5uJJLqSKxLymvpi[/img][img width=24,height=24]https://lh5.googleusercontent.com/EeYLvel9HmsnYD7ZRVm-HBQtblHhlB35cdQzXdG11nyuG3R7BCgnyC_l3L8aKn1R4wNkQnlMJHA72jcGN8n5f2RRahLZMiuy01yMfDJFEssc0gxkkfajbgHSyt1KTilGP0RyH5NA[/img][/td][td]Enhance your construction by chanigng the line thickness and color of the graphs and areas using the [i]Style Bar [/i]of the selected object.[/td][/tr][tr][td]7.[/td][td][/td][td]Observe the relation of [i]f'(x) [/i]and the monotonicity of [i]f(x)[/i].[/td][/tr][/table]