Unit route
Study lessons in order, complete the pathway selected by diagnostic evidence, conduct the investigation, then demonstrate mastery. Reassessment follows correction and reflection.
Weeks 19, 20, 21 · 7 detailed lessons
Contextual Applications of Derivatives
How do derivatives describe motion, related quantities, sensitivity, and local approximation in authentic contexts?
Pathways
Lesson 01 · Week 19
Position, Velocity & Acceleration
Position, velocity, and acceleration are successive layers of change. Their signs and zeros describe direction, speed changes, turning, and concavity, while their units distinguish the quant…
Lesson 02 · Week 19Interpreting Derivatives in Context
A contextual derivative statement must identify the input, output, instant, units, and practical meaning. Positive and negative values describe direction of change, not whether the quantity …
Lesson 03 · Week 19Related Rates: Geometry and Measurement
Related-rates problems connect quantities that change together. An equation describes the geometric or physical relationship; differentiating with respect to time turns that relation into a …
Lesson 04 · Week 20Related Rates: Volume and Flow
Related-rates problems connect quantities that change together. An equation describes the geometric or physical relationship; differentiating with respect to time turns that relation into a …
Lesson 05 · Week 20Linearization and Tangent-Line Approximation
Linearization uses the tangent line as a nearby approximation. Accuracy improves near the center point and depends on curvature and input distance.…
Lesson 06 · Week 21Differentials and Propagated Error
Linearization uses the tangent line as a nearby approximation. Accuracy improves near the center point and depends on curvature and input distance.…
Lesson 07 · Week 21Sensitivity, Units & Model Validation
A contextual derivative statement must identify the input, output, instant, units, and practical meaning. Positive and negative values describe direction of change, not whether the quantity …