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Lesson Packs · Grade 12 · Mathematics

Concavity, Inflection Points and Curve Sketching

Students use the second derivative to find where a graph is concave up or concave down, locate inflection points, classify stationary points with the second derivative test, and sketch cubic and rational functions with a full curve-sketching checklist.

MathematicsGrade 12Unit 3 · Lesson 10G12-MAT-10
Slide 1
Concavity, Inflection Points and Curve Sketching — Slide 1
+34in the download
39slides: lesson, examples and worksheet
10worksheet questions
34marks in total
4 + 4worksheet + answer key pages

Learning objectives

  • Determine where a function is concave up or concave down from the sign of f″(x).
  • Find inflection points and classify stationary points with the second derivative test.
  • Sketch polynomial and rational functions using the domain, intercepts, asymptotes, extrema and inflection points.

What's inside

  • 39 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 Unit 3

All Grade 12 Mathematics lessons

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).

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