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Unit 5: Analytical Applications of Differentiation

Exploring Behaviors of Implicit Relations

Find the critical points of a curve defined implicitly, and use dy/dx and the second derivative in x, y and dy/dx to justify relative extrema and concavity.

Topic 5.12 · 10 min read

This lesson comes with the AP Calculus AB plan

In this lesson

  1. 01Critical points on a curve
  2. 02The first derivative test on an implicit curve
  3. 03Second derivatives in , , and
  4. 04Worked examples
  5. 05Where students lose points
  6. 06On the exam

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