Demonstrates Average and Instantaneous Rates of Change, and how AROC becomes IROC as [math]\Delta x \to 0[/math].

Select a function from the drop-down list. Or, you can enter a function in the "Your Function" box, then select it from the list.[br][br]Check or clear the "[color=#7f00ff]Secant Line[/color]" and/or "[color=#009900]Tangent Line[/color]" boxes to view or hide those lines.[br][br]Drag the "[color=#ff0000]a[/color]" point along the [math]x[/math]-axis to set the location of the point on the graph at which the rate of change is to be measured. Now change [math]\Delta x[/math] using the slider and observe the results.[br][br]You can see the rise-over-run graphic for the slope of either line by checking the brown "[color=#993300]Tangent Slope[/color]" and/or "[color=#993300]Secant Slope[/color]" boxes. This is only visible when its corresponding line is visible.[br][br]If you clear "[color=#800080]Show/Hide f(x)[/color]", the function graph will become very light and the [math]\frac{\Delta y}{\Delta x}[/math] structure of the [color=#7f00ff]secant line[/color] can be seen.[br][br]As you move the [math]\Delta x[/math] slider value toward zero, the [color=#7f00ff]secant line[/color] will approach the [color=#009900]tangent line [/color]. When [math]\Delta x[/math] equals zero, the [color=#7f00ff]secant line[/color] becomes undefined, but the [color=#009900]tangent line [/color] remains visible.