The Definition of the Derivative
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The gray secant line joins the fixed red point on the graph of 
to a movable black point on the curve. Drag the black point along the curve. The slopes of the secant lines approximate the slope of the tangent line, which is the derivative of the function at 
.
Contributed by: Jim Swift (March 2011)
Open content licensed under CC BY-NC-SA
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"The Definition of the Derivative"
http://demonstrations.wolfram.com/TheDefinitionOfTheDerivative/
Wolfram Demonstrations Project
Published: March 7 2011
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