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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.

4 Lessons
~4-5 hours
10 Practice Problems
Module Quiz

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

After the Lessons

Practice Problems

10 practice problems covering all module topics.

Practice Problems

Module Quiz

10-question quiz to test your understanding.

Take Module Quiz

Study Materials

Printable study guide and quick reference card.

Begin Module 5 →