Intuitive Graphing of Derivatives

A function is graphed below. The GREEN points control its shape. The YELLOW points can be dragged anywhere along the graph without changing tis shape. Each YELLOW point has a BLUE point lying above or below it, whose height matches the slope of the line segment through the YELLOW point. Move the BLUE points to make the slopes tangent to the function. Then slide the slider to extend the line segments and graph the true derivatives.