Local Extrema

Definition

Local extrema are the highest or lowest points on a graph within a specific interval. They occur when the slope of the function changes from positive to negative (for a local maximum) or from negative to positive (for a local minimum).

Related terms

Critical Points:

Critical points are the values where the derivative of a function is either zero or undefined. They can be potential locations for local extrema.

First Derivative Test:

The first derivative test is used to determine whether critical points correspond to local maxima, minima, or neither by analyzing the sign changes of the derivative around those points.

Absolute Extrema:

Absolute extrema are the highest or lowest points on an entire graph, not just within a specific interval. They can occur at endpoints or critical points.