Relative Extrema

Definition

Relative extrema are points on a graph where there is either a local maximum (highest point) or a local minimum (lowest point). These points are compared to their neighboring points rather than the entire graph.

Related terms

Critical Point: A point on a graph where its derivative is either zero or undefined, which could potentially correspond to a relative extremum.

First Derivative Test: A method used to analyze whether critical points on a graph correspond to relative maxima or minima based on the sign changes of the first derivative.

Absolute Extrema: The highest and lowest values of a function over its entire domain, including both local and global maximums and minimums.