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WMA12/01 Jun 2024, Question 9: Stationary Points, Increasing and Optimising

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

For the curve y = 2x^(3/2)(4 − x), x ≥ 0, with stationary point P and shaded regions R₁ and R₂ shown, find P's x coordinate and the value of k giving equal areas.

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

Part (a) · 4 marks

Use calculus to find the x coordinate of the stationary point P on the curve.

  1. 1y = 8x^(3/2) − 2x^(5/2)
  2. 2dy/dx = 12x^(1/2) − 5x^(3/2)
  3. 3Set dy/dx = 0: x^(1/2)(12 − 5x) = 0
  4. 4x ≠ 0 at P, so x = 12/5

Answerx = 12/5

Part (b) · 4 marks

Given R₁ and R₂ have equal areas, use calculus to find the exact value of k.

  1. 1∫(8x^(3/2) − 2x^(5/2)) dx = (16/5)x^(5/2) − (4/7)x^(7/2)
  2. 2Equal areas above and below the axis mean the integral from 0 to k is 0
  3. 3(16/5)k^(5/2) − (4/7)k^(7/2) = 0
  4. 4k^(5/2)(16/5 − (4/7)k) = 0, so k = (16/5)(7/4) = 28/5

Answerk = 28/5

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Also searched as: WMA12 June 2024 · WMA12/01 · wma12 jun24 · IAS Maths Pure Mathematics 2 June 2024 · question 9.
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