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4MA1/1HR Jun 2018, Question 19: Stationary Points and Turning Points

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

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The question, in short

For the cubic y = x³ − 27x + k with k positive and less than 54, use differentiation to find b − d, where A(a, b) is the maximum and B(c, d) the minimum.

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Solution · 6 marks

  1. 1dy/dx = 3x² − 27
  2. 23x² − 27 = 0, so x = −3 or x = 3
  3. 3Maximum at x = −3: b = −27 + 81 + k = 54 + k
  4. 4Minimum at x = 3: d = 27 − 81 + k = k − 54
  5. 5b − d = (54 + k) − (k − 54) = 108

Answer108

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