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WMA12/01 Jan 2021, Question 2: Stationary Points and Turning Points

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

For the curve y = x³ − x² − 16x + 2, use calculus to locate the stationary points and then determine what type each one is.

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

Part (a) · 4 marks

Differentiate y = x³ − x² − 16x + 2 and solve for the x coordinates where the gradient is zero.

  1. 1dy/dx = 3x² − 2x − 16
  2. 2At stationary points 3x² − 2x − 16 = 0
  3. 3(3x − 8)(x + 2) = 0
  4. 4x = 8/3 or x = −2

Answerx = 8/3 and x = −2

Part (b) · 3 marks

Use the second derivative to classify each stationary point found in part a as maximum, minimum or otherwise.

  1. 1d²y/dx² = 6x − 2
  2. 2At x = 8/3: d²y/dx² = 16 − 2 = 14 > 0, so a minimum
  3. 3At x = −2: d²y/dx² = −12 − 2 = −14 < 0, so a maximum

Answerx = 8/3 is a minimum (d²y/dx² = 14 > 0); x = −2 is a maximum (d²y/dx² = −14 < 0)

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