Decreasing function Calculator
Defines a decreasing function as one whose outputs fall as inputs increase on an interval.
Formula first
Overview
Defines a decreasing function as one whose outputs fall as inputs increase on an interval. It explains the calculus condition behind the rule and how that condition controls graph behavior. Students should use it to decide what can be concluded from derivatives, extrema, or interval hypotheses.
Symbols
Variables
result = result
Apply it well
When To Use
When to use: Use this when a calculus problem asks about monotonicity, concavity, local extrema, mean-value-theorem consequences, or indeterminate quotient forms.
Why it matters: These tests turn derivative information into clear statements about graph behavior and limits.
Avoid these traps
Common Mistakes
- Skipping a required continuity or differentiability condition.
- Using a one-point derivative value to conclude behavior on a whole interval.
One free problem
Practice Problem
Is f(x)=-x decreasing on all real numbers?
Solve for: result
Hint: Check the definition, derivative sign, or limit form before concluding.
The full worked solution stays in the interactive walkthrough.
References
Sources
- OpenStax, Calculus Volume 1, Section 4.5: Derivatives and the Shape of a Graph, accessed 2026-04-09
- Wikipedia: Monotonic function, accessed 2026-04-09
- IUPAC Gold Book
- Wikipedia: Decreasing function