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Inflection Point

curve concave upward downward

In mathematics, an inflection point is a point on a curve at which the curve changes from being concave upward to being concave downward, or vice versa. A concave upward curve can be thought of as one that would hold water, while a concave downward curve is one that would not. An important qualification is that the curve must have a unique tangent line at the point of inflection. This means that the curve must change smoothly from concave upward to concave downward, not abruptly. As a practical example of an inflection point consider an "s-curve" on the highway. Precisely at the inflection point the driver changes from steering left to steering right, or vice versa as the case may be.

In calculus, an inflection point is characterized by a change in the sign of the second derivative. Such a sign change occurs when the second derivative passes through zero or becomes infinite.

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