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Mathematics · Grade 11

Applications and Optimization

Learners use derivatives to analyze and optimize. They find critical points, classify extrema with the first- and second-derivative tests, study concavity and inflection points, locate absolute extrema on closed intervals, solve optimization problems such as designing a box or a fence, apply the Mean Value Theorem, and decide when a moving object speeds up or slows down. An optional honors lesson introduces L'Hôpital's rule.

  • 5 lessons
  • About 160 minutes
  • Applications and optimization check: 12 questions
  • Ways to answer: choose an answer, type a number, place on a number line, put in order, sort into groups and true or false
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What learners will discover

  • Find critical points and use the first-derivative test to find intervals of increase and decrease and local extrema.
  • Use the second derivative to determine concavity and inflection points, and apply the second-derivative test.
  • Find absolute extrema on closed intervals and solve optimization problems, justifying that the answer is optimal.
  • Apply the Mean Value Theorem and analyze motion, including when an object speeds up or slows down.

Lessons

  1. Critical points and the first-derivative test 5 steps3 practiceabout 34 min
  2. Concavity and the second derivative 5 steps3 practiceabout 30 min
  3. Absolute extrema and optimization 5 steps3 practiceabout 40 min
  4. The Mean Value Theorem and motion 5 steps3 practiceabout 32 min
  5. Going further (honors): L'Hôpital's rule 4 steps2 practiceabout 24 min
  6. Applications and optimization check 12 questions at the end

Keep exploring

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Guide for grown-ups