Concavity

Definition

Concavity describes whether a graph opens upward (concave up) or downward (concave down). It indicates whether the graph is curving upwards like an "U" shape or downwards like an "n" shape.

Related terms

Inflection Point:

An inflection point occurs where there is a change in concavity on a graph. At this point, the graph transitions from being concave up to concave down or vice versa.

Second Derivative Test:

The second derivative test helps determine if critical points on a graph represent local maxima or minima by analyzing changes in concavity.

Point of Inflection:

A point of inflection is a specific type of inflection point where the graph changes concavity and has no local maxima or minima.