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Investigation 8: The Derivative
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Tangent
The line segment joining P and
Q is called a secant line. Moving the point Q along the curve
toward P, allows you to see that as Q approaches P,
the secant line gets closer and closer to the tangent line. The slope of the
curve at P is approximately the slope of the line segment
.
The approximation becomes more accurate as Q moves along the curve toward
P.
The slope of the curve at P is defined as the limit of the slope of PQ as Q approaches P along the curve. This is denoted as follows:
