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4MA1/2H Jun 2025, Question 17: Differentiation and turning points

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

For y = 4x³ + 5x² + 2x, find dy/dx, then find the coordinates of the turning points.

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

Part (a) · 2 marks

Find dy/dx.

  1. 1d/dx(4x³) = 12x²
  2. 2d/dx(5x²) = 10x
  3. 3d/dx(2x) = 2
  4. 4dy/dx = 12x² + 10x + 2

Answer12x² + 10x + 2

Part (b) · 4 marks

Find the coordinates of the turning points.

  1. 112x² + 10x + 2 = 0
  2. 26x² + 5x + 1 = 0
  3. 3(3x + 1)(2x + 1) = 0
  4. 4x = −1/2 or x = −1/3
  5. 5y = 4(−1/2)³ + 5(−1/2)² + 2(−1/2) = −1/4
  6. 6y = 4(−1/3)³ + 5(−1/3)² + 2(−1/3) = −7/27

Answer(−1/2, −1/4), (−1/3, −7/27)

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

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