Curve Sketching
The curve-sketching checklist
Information from each derivative
Complete example: $f(x) = x^4 - 4x^3$
Complete example: $f(x) = \dfrac{x^2}{x^2 - 1}$
Sketching from $f'$ and $f''$ graphs
Key shapes to recognize
AP exam tips
- •
- •
- •
- •
- •
Vocabulary
Unit 5 topics
Unit 5 overview15.1 Using the Mean Value Theorem25.2 Extreme Value Theorem and Critical Points35.3 Determining Intervals of Increasing and Decreasing45.4 Using the First Derivative Test55.5 Using the Candidates Test for Absolute Extrema65.6 Determining Concavity and Points of Inflection75.7 Using the Second Derivative Test85.8 Sketching Curves of Functions and Their Derivatives95.9 Connecting f, f', and f''105.10 Solving Optimization Problems