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0580/43 May/Jun 2026, Question 20: Stationary Points and Turning Points

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 8 marks

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The question, in short

For the cubic y = 8x³ − 6x + 5, locate its turning points with full working, then classify each given turning point as maximum or minimum and justify the choice.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 5 marks

Work out the coordinates of the stationary points on y = 8x³ − 6x + 5, showing every step of the method.

  1. 1dy/dx = 24x² − 6
  2. 224x² − 6 = 0 ⇒ x² = 1/4
  3. 3x = 1/2 or x = −1/2
  4. 4x = 1/2: y = 8(1/8) − 3 + 5 = 3
  5. 5x = −1/2: y = −1 + 3 + 5 = 7
  6. 6Turning points (1/2, 3) and (−1/2, 7)

Answer(1/2, 3) and (−1/2, 7)

Part (b) · 3 marks

Using the turning points (1/2, 3) and (−1/2, 7), decide which is a maximum and which a minimum, explaining your reasoning.

  1. 1d²y/dx² = 48x
  2. 2At x = −1/2: 48 × (−1/2) = −24 < 0, so (−1/2, 7) is a maximum
  3. 3At x = 1/2: 48 × 1/2 = 24 > 0, so (1/2, 3) is a minimum

Answer(−1/2, 7) maximum and (1/2, 3) minimum, with correct reasons

Stuck on a step? Read the free lesson: Stationary Points and Turning Points

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Also searched as: 0580/43/M/J/26 · 0580_s26_qp_43 · 0580 s26 43 · question 20.
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