Graphs of Functions & Their Derivatives

This study guide covers increasing and decreasing functions using the first derivative, $f'(x)$. It explains how to find these intervals by solving inequalities ($f'(x) \geq 0$ for increasing, $f'(x) \leq 0$ for decreasing) and interpreting the graph of $f(x)$ and $f'(x)$. 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.