AP Calculus AB and BC glossary
Increasing function
Also called: Decreasing function, Monotonic
A function is increasing on an interval where its derivative is positive and decreasing where its derivative is negative. Increasing behaviour is a property of an interval, not of a single point.
The method is a sign chart for , using the critical points as dividers. Report the answer as intervals of values, since that is what the definition describes.
The mistake
Reporting where the function is increasing using values or naming a single point. The answer to an increasing or decreasing question is always a set of intervals on the axis.
Appears in: Unit 5: Analytical Applications