Increasing/Decreasing Functions

Definition

An increasing function is one in which the values of the function increase as the input increases. A decreasing function is one in which the values of the function decrease as the input increases.

Related terms

Local Maximum/Minimum: A local maximum occurs when a function reaches its highest point within a specific interval, while a local minimum occurs when a function reaches its lowest point within that interval.

Critical Points:

These are points on a graph where either the derivative is zero or does not exist. They can be used to determine whether a function is increasing or decreasing.

Inflection Points:

These are points on a graph where the concavity changes. They can indicate transitions between increasing and decreasing behavior.