Third derivative

Definition

The third derivative of a function represents how quickly the curvature (second derivative) is changing at any given point. It helps determine whether a graph has points of inflection.

Related terms

Fourth derivative: The fourth derivative measures how quickly the rate of change (third derivative) is changing along with x-values. It provides information about higher-order concavity.

Concave up: A graph is concave up when its curvature (second derivative) is positive throughout an interval.

Concave down: A graph is concave down when its curvature (second derivative) is negative throughout an interval.