[b]Instructions:[/b][br][br]In the following applet, the graph of the function [color=#1551b5]f(x) = cos(x)[/color] is shown.[br]You'll also notice there are [color=#c51414]9 red points[/color].[br][color=#c51414]The y-coordinate of each red point is displayed.[/color][br][color=#c51414]These y-coordinate of each red point[/color] is the slope of the line drawn to the graph of this function (and appears either directly above or below it).[br][br]Your job is to [color=#c51414]move these 9 red points up and/or down[/color] so that [b]ALL the black lines APPEAR TANGENT to the graph of the function[/b] [color=#1551b5]y = cos(x)[/color].[br]Do this task now.[br][br]After completing this task, check the "Show Graph of Derivative Function" checkbox to see how you did.[br]The graph of the derivative of this function is shown in purple.[br][br]Please see the follow-up questions below this applet and answer them.

[b]Questions:[/b][br][br]1) Does the graph of this derivative function look familiar?[br]2) Write a function rule, f'(x), for the derivative of this function.[br][br]3) Prove, using the definition of a derivative, that the derivative function you wrote in (2) above is correct.