References: Derivative Tests and Concavity

1. First derivative test - Wikipedia - Statement and application of the first derivative test for classifying critical points as local maxima, minima, or neither. Core reference for this chapter.

2. Second derivative test - Wikipedia - Using the second derivative to classify critical points, including cases where the test is inconclusive. Complements the first derivative test comparison in this chapter.

3. Inflection point - Wikipedia - Definition, detection methods, and relationship to concavity changes. Essential for the chapter's treatment of concavity analysis and inflection point identification.

4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Sections 4.3-4.4 cover increasing/decreasing functions, concavity, inflection points, and both derivative tests with sign chart methods.

5. Thomas' Calculus (15th Edition) - Joel Hass, Christopher Heil, Maurice Weir - Pearson - Sections 4.3-4.4 provide systematic treatment of monotonicity, concavity, and curve shape analysis with detailed examples.

6. First Derivative Test - Paul's Online Math Notes - Sign chart construction and interpretation for determining intervals of increase/decrease and classifying critical points.

7. Second Derivative Test and Concavity - Paul's Online Math Notes - Concavity analysis, inflection point detection, and the second derivative test with comprehensive worked examples.

8. First and Second Derivative Tests - Khan Academy - Interactive practice on using both derivative tests to classify critical points, with AP-aligned problems.

9. Concavity and Inflection Points - Professor Leonard - Thorough lecture on second derivative analysis including sign charts, concavity intervals, and inflection point identification.

10. Concavity and the Second Derivative - Whitman College Calculus - Open-source section with formal definitions, proofs, and exercises on concavity and inflection points.