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Section 2.3 Interpretations of the Derivative

In the previous sections we defined the derivative as the slope of a tangent line, using a particular limit. This allows us to compute “the slope of a curve”  1 Again — recall that we are being a little sloppy with this term — we really mean “The slope of the tangent line to the curve”. and provides us with one interpretation of the derivative. However, the main importance of derivatives does not come from this application. Instead, (arguably) it comes from the interpretation of the derivative as the instantaneous rate of change of a quantity.