Written by the Fiveable Content Team • Last updated September 2025
Verified for the 2026 exam
Verified for the 2026 exam•Written by the Fiveable Content Team • Last updated September 2025
Definition
In calculus, when we say that a function is increasing, it means that as x values increase, so do y values. In other words, the graph goes up from left to right.
When a function is decreasing, it means that as x values increase, y values decrease. It's like going down stairs where each step takes you lower than before.
Local Maximum/Minimum: A local maximum occurs when there's a peak in the graph and it starts descending after reaching that point. Similarly, a local minimum happens when there's a dip in the graph and it starts ascending after reaching that point.
Monotonic: A function is monotonic if it's either always increasing or always decreasing. It's like climbing a staircase where each step takes you higher, or descending a staircase where each step takes you lower, without any plateaus or changes in direction.