Module 4: Applications of Derivatives I
Put your differentiation skills to work! This module covers real-world applications including related rates, linear approximation, finding extreme values, and the powerful Mean Value Theorem.
Your Progress
Learning Objectives
By the end of this module, you will be able to:
- Solve related rates problems by differentiating with respect to time
- Use linearization and differentials to approximate function values
- Find absolute and local extreme values using critical points
- State and apply the Mean Value Theorem and Rolle's Theorem
Module Lessons
Related Rates
Use implicit differentiation with respect to time to solve problems where multiple quantities change simultaneously.
40-50 minutes
Linear Approximation and Differentials
Approximate function values using the tangent line, and understand differentials as a tool for estimation.
30-40 minutes
Extreme Values and Critical Points
Find absolute and local maxima and minima using the Extreme Value Theorem and critical points.
35-45 minutes
The Mean Value Theorem
Understand the MVT and Rolle's Theorem, and see why they are among the most important theoretical results in calculus.
30-40 minutes
After the Lessons
Practice Problems
Apply what you have learned with 10 practice problems covering all module topics.
Practice ProblemsStudy Materials
Printable study guides and quick reference cards for exam prep.