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Lesson Packs · Grade 12 · Mathematics

The Derivative and Tangent Lines

Students move from the average to the instantaneous rate of change, see the tangent line as the limit of secant lines, find derivatives from first principles, write equations of tangent lines and meet a function that is continuous but not differentiable.

Unit 2 · Lesson 4 · Derivatives

Preview

The Derivative and Tangent Lines — Slide 1
  • The Derivative and Tangent Lines — Slide 4
    Slide 4
  • The Derivative and Tangent Lines — Slide 9
    Slide 9
  • The Derivative and Tangent Lines — Slide 17
    Slide 17
  • The Derivative and Tangent Lines — Slide 18
    Slide 18
  • The Derivative and Tangent Lines — Worksheet, page 1
    Worksheet, page 1
  • The Derivative and Tangent Lines — Answer key, page 1
    Answer key, page 1

Learning objectives

  • Explain the difference between the average rate of change and the instantaneous rate of change of a function.
  • Find a derivative from first principles, using f′(x) = lim(h→0) (f(x + h) − f(x))/h.
  • Write the equation of a tangent line, and recognize a function that is continuous but not differentiable.

What's inside

  • 38 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 10 worksheet questions (33 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).

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