Sketching Derivatives of Freehand Drawn Functions

Shown below are 3 hand-drawn function graphs. Each function is named [math]f[/math]. Complete the following steps for the first graph (for now).[br][list][*]Use the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool to drag [color=#1e84cc][b]point [i]A[/i][/b][/color] along [math]f[/math]. [/*][*]Use the POINT [icon]https://www.geogebra.org/images/ggb/toolbar/mode_point.png[/icon] tool to plot the locations of several key points that you know lie on the graph of the derivative of [math]f[/math]. [/*][/list][b]Note:[/b] The next 3 steps are illustrated in the video below the first app.[br][list][*]Use the PEN [icon]https://www.geogebra.org/images/ggb/toolbar/mode_pen.png[/icon] tool to draw a sketch of what you think the graph of [math]f'[/math] looks like. [/*][*]Plot the point [math]\left(x\left(A\right),m\right)[/math]. This point lies on the graph of [math]f'[/math]. [/*][*]Right click on the point you plotted in the last step. Select [b]SHOW TRACE[/b]. Then drag [i][b][color=#1e84cc]A [/color][/b][/i]around the graph slowly. [/*][/list][br][b]Question: [/b]Explain why the point [math]\left(x\left(A\right),m\right)[/math] lies on the graph of [math]f'[/math]. Also, how did you do?
After completing the steps above, right click on the point you plotted in the last step. Select SHOW TRACE. Then drag A around the graph slowly. How did you do?
Last 3 steps: Quick silent demo
Try to sketch the graph of f' here!
What would the graph of f' look like here?
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Information: Sketching Derivatives of Freehand Drawn Functions