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5.11 Solving 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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To solve an optimization problem completely, students first define variables, write the quantity to optimize, use the given constraints to rewrite that quantity in terms of one variable, and then use derivatives to locate maxima or minima. After finding critical points, you must justify that the point found actually gives the desired extreme value, often with the First Derivative Test, Second Derivative Test, or Candidates Test if an interval is given. A final answer should always be stated in context, not just as an x-value.

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 ProblemsPreview lesson
  11. 5.11Solving Optimization ProblemsThis lesson
  12. 5.12Exploring Behaviors of Implicit RelationsPreview lesson

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