Graphs of Functions & Their Derivatives

Sarah Miller

Sarah Miller

5 min read

Study Guide Overview

This study guide covers increasing and decreasing functions using the first derivative, f(x)f'(x). It explains how to find these intervals by solving inequalities (f(x)0f'(x) \geq 0 for increasing, f(x)0f'(x) \leq 0 for decreasing) and interpreting the graph of f(x)f(x) and f(x)f'(x). The guide includes a worked example, practice questions, a glossary of key terms like critical points, and key takeaways summarizing the first derivative test and graphical analysis techniques.