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.
Analogy
Think of driving up or down a hill. If you're going up (increasing), your altitude is getting higher as you move forward. If you're going down (decreasing), your altitude is getting lower as you move forward.
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.
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