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Lesson Packs · Grade 12 · Mathematics

Increasing and Decreasing Functions and Extrema

Students use the sign of the first derivative to find where a function is increasing or decreasing, locate critical points, classify local maxima and minima with the first derivative test and a sign table, and find absolute extrema on a closed interval.

Unit 3 · Lesson 9 · Applications of Derivatives

Preview

Increasing and Decreasing Functions and Extrema — Slide 1
  • Increasing and Decreasing Functions and Extrema — Slide 4
    Slide 4
  • Increasing and Decreasing Functions and Extrema — Slide 9
    Slide 9
  • Increasing and Decreasing Functions and Extrema — Slide 17
    Slide 17
  • Increasing and Decreasing Functions and Extrema — Slide 18
    Slide 18
  • Increasing and Decreasing Functions and Extrema — Worksheet, page 1
    Worksheet, page 1
  • Increasing and Decreasing Functions and Extrema — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Use the sign of f′(x) to find the intervals on which a function is increasing or decreasing.
  • Find critical points and classify them as local maxima, local minima or neither with the first derivative test.
  • Find the absolute maximum and minimum values of a continuous function on a closed interval.

What's inside

  • 38 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.

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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).

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