Tangent, Curvature, Slope, Derivative

Tangent, in geometry, the tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point. It may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve as the second point

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What is the graph of the tangent line to the curve if the first derivative of the function at its critical point is undefined? - Quora

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