Skip to content

References: Curve Sketching

  1. Curve sketching - Wikipedia - Systematic procedure for analyzing and sketching function graphs using calculus tools. Directly covers the complete sketching methodology taught in this chapter.

  2. Critical point (mathematics) - Wikipedia - Types of critical points and their role in graph analysis. Supports the chapter's integration of first and second derivative information into complete sketches.

  3. Concave function - Wikipedia - Formal definitions of concavity with visual examples and relationship to second derivatives. Provides theoretical depth for the concavity analysis in curve sketching.

  4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Section 4.5 presents the complete curve sketching procedure with a structured checklist and numerous worked examples of increasing complexity.

  5. Thomas' Calculus (15th Edition) - Joel Hass, Christopher Heil, Maurice Weir - Pearson - Section 4.6 covers graphing with calculus and calculators, emphasizing how to combine analytical tools into a complete picture.

  6. Curve Sketching - Paul's Online Math Notes - Complete worked examples following a systematic sketching procedure with domain, intercepts, symmetry, asymptotes, and derivative analysis.

  7. Analyzing Functions with Calculus - Khan Academy - Practice combining first and second derivative information to sketch function graphs, aligned to AP exam expectations.

  8. Curve Sketching Strategy - Professor Leonard - Comprehensive lecture walking through multiple complete curve sketching examples from start to finish.

  9. Graphing Calculator - Desmos - Free online graphing tool for verifying hand-drawn curve sketches and exploring how parameter changes affect graph features.

  10. Summary of Curve Sketching - Whitman College Calculus - Open-source section integrating all calculus-based graphing techniques into a unified approach with exercises.