# Inflection Point

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.

## Additional topics

Science EncyclopediaScience & Philosophy: *Incomplete dominance* to *Intuitionism*