[color=#0a971e][b]Instructions:[/b][/color] In the following applet, the graph of the function [color=#0a971e]y = sin(x)[/color] is shown. You'll also notice there are [color=#c51414]9 red points[/color]. The [color=#c51414]y-coordinate of each red point[/color] is displayed. These [color=#c51414]y-coordinate of each red point[/color] is the slope of the line drawn to the [color=#0a971e]graph of this function[/color] (and appears either directly above or below it). Your job is to move these [color=#c51414]9 red points[/color] up and/or down so that [b]ALL the black lines APPEAR TANGENT[/b] to the [color=#0a971e]graph of the function y = sin(x)[/color]. Do this task now. After completing this task, check the [color=#c51414]"Show Graph of Derivative Function" [/color]checkbox to see how you did. [color=#c51414]The graph of the derivative of this function is shown in red. [/color] Please see the follow-up questions below this applet and answer them.

[b][color=#c51414]Questions:[/color] [/b] 1) [color=#c51414]Does the graph of this derivative function look familiar? [/color] 2) [color=#c51414]Write a function rule, f'(x), for the derivative of this function.[/color] 3) Prove, using the definition of a derivative, that the derivative function you wrote in (2) above is correct.