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5.10 Introduction to Optimization Problems

Part of Analytical Applications of Differentiation in AP® Calculus BC. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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An optimization problem asks for the maximum or minimum value of a quantity subject to some condition or constraint. In calculus, the goal is usually to write the quantity to be optimized as a function of one variable, find its critical points, and then determine which one gives the greatest or least value. Optimization problems are important because they show how derivatives can solve real problems involving area, volume, cost, revenue, distance, and many other quantities.

In this unit

12 lessons

  1. 5.1Using the Mean Value TheoremPreview lesson
  2. 5.2Extreme Value Theorem, Global Versus Local Extrema, and Critical PointsPreview lesson
  3. 5.3Determining Intervals on Which a Function Is Increasing or DecreasingPreview lesson
  4. 5.4Using the First Derivative Test to Determine Relative (Local) ExtremaPreview lesson
  5. 5.5Using the Candidates Test to Determine Absolute (Global) ExtremaPreview lesson
  6. 5.6Determining Concavity of Functions over Their DomainsPreview lesson
  7. 5.7Using the Second Derivative Test to Determine ExtremaPreview lesson
  8. 5.8Sketching Graphs of Functions and Their DerivativesPreview lesson
  9. 5.9Connecting a Function, Its First Derivative, and Its Second DerivativePreview lesson
  10. 5.10Introduction to Optimization ProblemsThis lesson
  11. 5.11Solving Optimization ProblemsPreview lesson
  12. 5.12Exploring Behaviors of Implicit RelationsPreview lesson

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