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4PM1/01R Jun 2020, Question 4: Stationary Points and Turning Points

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 6 marks

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The question, in short

For the curve y = x³ − 3x² − 24x + 6, use calculus to locate the stationary points and then classify each one, giving reasons.

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

Part (a) · 4 marks

Differentiate y = x³ − 3x² − 24x + 6, solve for x where the gradient is zero, and state the coordinates of each stationary point.

  1. 1dy/dx = 3x² − 6x − 24
  2. 23(x + 2)(x − 4) = 0
  3. 3x = −2 or x = 4
  4. 4y = 34 or y = −74: (−2, 34) and (4, −74)

Answer(−2, 34) and (4, −74)

Part (b) · 2 marks

Use the second derivative or a gradient test to decide whether each stationary point is a maximum or minimum, justifying each conclusion.

  1. 1d²y/dx² = 6x − 6
  2. 2x = −2: d²y/dx² = −18 < 0 ⇒ maximum
  3. 3x = 4: d²y/dx² = 18 > 0 ⇒ minimum

Answer(−2, 34) is a maximum and (4, −74) is a minimum

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