AUTHOR: Sarab DATE: 2:28:00 PM ----- BODY:

This image indicates the 2 high level abstractions involved in determining a derivative. The secant line is an approximation to the desired slope at a particular point along the curve. The secant line consists of 2 points: 1 point designates the point on the curve where we would like to find the slope, the other point represents the reference point from where we can measure change in y value over change in x value. As the second point is made to be closer and closer to the point we want to determine the value of, we get closer and closer approximations to the derivative, or slope at that given point.

The next image illustrates this far better than I can describe in prose.


Unfortunately the speed is a bit too fast, but you can see that the second point on the curve is made closer and closer to the first point, and how that eventually yields the tangent line/derivative/slope at that given point.

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