---
id: mat-03-derivative-applications
title: "Applications of derivatives"
---

# Applications of derivatives

## Increasing decreasing and extrema
Use the sign of the derivative to determine where a function increases or decreases, and locate maxima or minima.

## Optimization workflow
Typical steps:
1) define the objective function
2) compute derivative
3) find critical points
4) test candidates (including endpoints if relevant)
5) interpret the solution

## Related rates idea
Differentiate an equation relating variables with respect to time to connect their rates of change.

## Error and sensitivity
Derivatives quantify sensitivity: how much output changes per unit input.