Average vs. Instantenous Rates of Change
Demonstrates Average and Instantaneous Rates of Change, and how AROC becomes IROC as .
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. Check or clear the "Secant Line" and/or "Tangent Line" boxes to view or hide those lines. Drag the "a" point along the -axis to set the location of the point on the graph at which the rate of change is to be measured. Now change using the slider and observe the results. You can see the rise-over-run graphic for the slope of either line by checking the brown "Tangent Slope" and/or "Secant Slope" boxes. This is only visible when its corresponding line is visible. If you clear "Show/Hide f(x)", the function graph will become very light and the structure of the secant line can be seen. As you move the slider value toward zero, the secant line will approach the tangent line . When equals zero, the secant line becomes undefined, but the tangent line remains visible.