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Lesson Packs · Grade 12 · Mathematics

Optimization Problems

Students solve optimization problems with derivatives: they define variables, use a constraint to write a one-variable objective function with a realistic domain, find its critical points, and justify the maximum or minimum with the second derivative or the endpoints.

Unit 3 · Lesson 11 · Applications of Derivatives

Preview

Optimization Problems — Slide 1
  • Optimization Problems — Slide 4
    Slide 4
  • Optimization Problems — Slide 8
    Slide 8
  • Optimization Problems — Slide 16
    Slide 16
  • Optimization Problems — Slide 17
    Slide 17
  • Optimization Problems — Worksheet, page 1
    Worksheet, page 1
  • Optimization Problems — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Translate a word problem into an objective function of one variable, using a constraint and a realistic domain.
  • Use derivatives to find the maximum or minimum value of the objective function.
  • Justify an optimum with the second derivative test or by checking the endpoints, and interpret it in context.

What's inside

  • 40 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 10 worksheet questions (34 marks) with step-by-step solutions
  • Printable worksheet (4 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

More lessons in this unit

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

Do downloads count toward my plan?

Yes. Sign in with your free KiwiBee account to download. Each download counts toward your plan's daily and monthly download limit, the same as worksheets.