Module 5: Applications of Derivatives II
Continue applying derivatives to analyze function behavior. Learn the first and second derivative tests, master curve sketching, and solve optimization problems.
Your Progress
Lessons 1-4
Practice
Module Quiz
Review
Learning Objectives
By the end of this module, you will be able to:
- Apply the First Derivative Test to classify critical points
- Use the Second Derivative Test and determine concavity
- Sketch curves using derivatives, intercepts, and asymptotes
- Solve optimization problems from real-world contexts
Module Lessons
1
First Derivative Test
Use the sign of f' to classify critical points as local maxima, local minima, or neither.
30-40 minutes
2
Second Derivative and Concavity
Analyze concavity, find inflection points, and apply the Second Derivative Test.
35-45 minutes
3
Curve Sketching
Combine all derivative tools to produce accurate sketches of functions.
40-50 minutes
4
Optimization Problems
Solve applied max/min problems from geometry, business, and physics.
40-50 minutes