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In an earlier video ( • Tangent Line in Geogebra ), we looked at how to sketch a tangent line to match a graph of a function at a point. Once we had the tangent line, we could use the line to estimate the slope of the tangent line. That slope is called the derivative of the original function.
In this video, we consider a sequence of second points from the graph to find a slope that is the limit of average rates of change. This is how we will define the derivative. The derivative at a point equals the limit of the average rate of change of the function between that point and a second point as the second point gets closer and closer to the point of interest.