Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Use first and second derivative tests to distinguish between maxima and minima and justify conclusions
Learning Objective/s:
  • Apply the first derivative test to classify stationary points as maxima, minima, or points of inflection.
  • Apply the second derivative test and interpret concavity to confirm classifications.
  • Justify conclusions with clear reasoning and recognise when a test is inconclusive.
  • Solve worked examples and avoid common pitfalls in derivative testing.
Materials Needed:
  • Projector or interactive whiteboard
  • Graphing calculators or Desmos access
  • Printed worksheet with practice problems
  • Set of function cards for group activity
  • Whiteboard markers and erasers
 Introduction:
Begin with a quick visual of a cubic curve showing peaks and valleys to spark curiosity. Review that stationary points occur where f′(x)=0 and recall how to compute derivatives. Explain that today students will use first and second derivative tests to determine whether these points are maxima, minima, or points of inflection, and will be able to justify their conclusions.
Lesson Structure:
  1. Do‑now (5'): Short worksheet identifying stationary points from given graphs (checks prior knowledge).
  2. Mini‑lecture (10'): Review first derivative test with sign charts and demonstrate on the board.
  3. Guided practice (12'): Work through the example f(x)=x³‑3x²+2, students fill each step of the first derivative test.
  4. Second derivative test (8'): Explain concavity, compute f''(c) and interpret; students verify the example.
  5. Collaborative activity (15'): In groups, use function cards to classify stationary points using both tests; teacher circulates for support.
  6. Quick check (5'): Exit ticket – students state which test they used for a given point and why.
Conclusion:
Summarise that the sign change of f′ determines the type of extremum and that f″ indicates concavity, noting when each test fails. Collect exit tickets as a retrieval check. Assign homework: complete the three practice questions from the notes.