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 22, 23, 24 · 7 detailed lessons
Analytical Applications & Optimization
How do derivatives reveal increasing behavior, extrema, shape, and optimal decisions?
Pathways
Lesson 01 · Week 22
Absolute and Local Extrema
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 02 · Week 22The Mean Value Theorem
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 03 · Week 22Increasing and Decreasing Intervals
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 04 · Week 23First Derivative Test
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 05 · Week 23Concavity and Points of Inflection
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 06 · Week 24Second Derivative Test and Curve Analysis
Derivative sign charts organize global behavior. Critical numbers, endpoints, and nondifferentiable points divide the domain into intervals where monotonicity and concavity can be tested.…
Lesson 07 · Week 24Optimization and Design Constraints
Optimization converts constraints into a one-variable objective, identifies the feasible domain, and compares all candidates—including endpoints. The final result must be interpreted in cont…