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Determine whether the statement is true or false. A tangent line to a curve y=f(x) is a particular kind of secant line to the curve.

User Gaven
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Final answer:

The statement is false; a tangent line touches the curve at one point and represents the instantaneous rate of change at that point, while a secant line intersects the curve at two or more points.

Step-by-step explanation:

The statement 'A tangent line to a curve y=f(x) is a particular kind of secant line to the curve' is false. A tangent line is a line that touches the curve at exactly one point, representing the instantaneous rate of change or slope of the curve at that point. On the other hand, a secant line intersects the curve at two or more points. The principle that the slope of a curve at a point equals the slope of a tangent line at that point can be applied in various contexts, including when working with velocity in physics as it relates to the slope of a position vs. time graph, or when finding instantaneous acceleration by taking a tangent line on a velocity graph.

User AkisC
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