Calculus AB Unit 5 - Applications of Derivatives

Unit 5: Applications of Derivatives

Unit 5 moves beyond calculating derivatives and focuses on how derivatives can be used to analyze and solve problems. Students investigate the relationship between functions and their derivatives, use derivatives to identify extrema, and apply derivative concepts to related rates and optimization problems. The unit also covers linear approximation, differentials, and motion involving position, velocity, and acceleration, helping students see how derivatives describe change in both mathematical and real-world contexts.

Lessons Included:

• Lesson 1: Graphing Derivatives
• Lesson 2: Extrema & Number Line Tests
• Lesson 3: Related Rates
• Lesson 4: Optimization
• Lesson 5: Linear Approximation & Differentials
• Lesson 6: Position, Velocity & Acceleration

Unit 5 includes 6 complete sections, 3 additional worksheets, a comprehensive review, and a unit exam, with answer keys included for all materials.