[size=200]Intuitive Derivative Graphing Exercise[/size]

[size=200]Below, the graph of a function is shown. [br][br][color=#38761d]The [b]LIGHT GREEN POINTS[/b] control the appearance of the entire graph. So to start & during this exercise, please don't touch these. [br][/color][br][color=#ff7700]The [b]ORANGE POINTS[/b] are points that lie on the graph of this function. These points can be dragged anywhere you like on the curve [i]prior to[/i] or [i]during[/i] your completion of this exercise. [/color][br][br][i]The Y-COORDINATE of each WHITE POINT is the same as the slope of the segment passing through (either the [b][color=#38761d]light green[/color][/b] or [color=#ff7700][b]orange[/b][/color]) point directly above it or directly below it.[/i][br][br]Given this information, position the WHITE POINTS in such a way that it causes the segment above it or below it to appear tangent to the graph of the function. [br][br]When you're done positioning the white points, use the pen[size=85] [img]https://www.geogebra.org/images/ggb/toolbar/mode_pen.png[/img] [/size]tool to sketch the derivative graph based upon your work.[br][br]To check your work, click "Check Your Work." [br][br]NOTE:[br]If you would like to try this exercise multiple times, simply use the delete icon [img]https://www.geogebra.org/images/ggb/toolbar/mode_delete.png[/img] to erase any previous sketches you made. Then, reposition any one (or more) of the four [b][color=#38761d]green points [/color][/b]to get an entirely different graph. [br][/size][size=200][br][i][b][color=#38761d]Just be sure not to move any green points in the middle of an exercise[/color][/b], at it will change the graph of the entire function. [br][br][/i][size=200]NOTE:[/size][br]If you do move any of the [b][color=#38761d]light green points[/color][/b] and the function graph disappears, simply refresh the page in your browser. [/size]

[size=200]Now you do it![br][br]Create 3 different configurations for the graph above and do the following for each.[br][br][list=1][*]Move the green points to create a different graph. [br][br][/*][*]Drag the slope to match the position function, and sketch the derivative. [br][br][/*][*]Finally, check your answer by finding the derivative and graphing using the extrema and x-intercepts.[br][br][/*][/list]Create a screen capture for each of the three configurations and email them to me for credit.[/size]