Instantaneous Rates of Change

What i found most confusing was how the book tried to use two different approaches when trying to explain that a derivative is the average rate of change at a point. I was personally confused when instantaneous velocity was defined to be the limit of the average velocity of the object over shorter and shorter periods of time intervals. Table 2.1 was just not that effective.

As a class I believe the most difficult area will be visualizing the derivative of the graph. At a point the derivative is the slope of the tangent line of the point on a graph. Again I believe we will need practice finding the derivative from data, a graph, and from an equation. But i think as we do some more examples it will become clearer.