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WMA12/01 Oct 2019, Question 1: Stationary Points and Turning Points

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Curve C is y = 2x²(x − 5). Use calculus to locate stationary points, then determine where the curve is increasing.

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

Part (a) · 4 marks

Differentiate y = 2x²(x − 5) and solve for the x coordinates where the gradient is zero.

  1. 1y = 2x³ − 10x²
  2. 2dy/dx = 6x² − 20x
  3. 3At stationary points 6x² − 20x = 0
  4. 42x(3x − 10) = 0
  5. 5x = 0 or x = 10/3

Answerx = 0 and x = 10/3

Part (b) · 2 marks

Using your stationary points, find the x values for which y is increasing.

  1. 1y is increasing where dy/dx = 2x(3x − 10) ≥ 0
  2. 2The parabola 6x² − 20x is positive outside its roots 0 and 10/3
  3. 3x ≤ 0 or x ≥ 10/3

Answerx ≤ 0 or x ≥ 10/3

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Also searched as: WMA12 October 2019 · WMA12/01 · wma12 oct19 · IAS Maths Pure Mathematics 2 October 2019 · question 1.
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