Increasing/Decreasing Functions and The First Derivative

Definition

An increasing function is one where as x increases, y also increases. A decreasing function is one where as x increases, y decreases. The first derivative can be used to determine whether a function is increasing or decreasing.

Related terms

Relative Extrema:

These are local maximum or minimum points on a graph.

Inflection Points:

These are points on a graph where the concavity changes from concave up to concave down, or vice versa.

Monotonicity Test: This test uses the sign of the first derivative to determine intervals where a function is increasing or decreasing.