The left-hand side of this applet is the same as the previous applet.
The right-hand side of this applet is a graph of the derivative function. As you use the slider [math]k[/math], note how the value of the derivative (slope of the tangent line) is modeled by the graph on the right.
As you use this applet you should focus on two main ideas: first, that the derivative of a function is itself a function, and second, that the graph of the derivative exists below the [math]x[/math]-axis when the slope of the tangent line is negative, exists above the [math]x[/math]-axis when the slope of the tangent line is positive, and crosses the [math]x[/math]-axis when the slope of the tangent line is zero.
