Lemmara logoLemmaraWorked solution

4MA1/1HR Jun 2022, Question 22: Stationary Points and Turning Points

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Curve y = x² − p/x with positive p has one minimum T. Use the given x-coordinate of T to determine p, then find k so that y = k touches y = x² − 16/x.

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

Part (a) · 4 marks

Given T has x-coordinate −3, determine the positive constant p.

  1. 1y = x² − p/x
  2. 2dy/dx = 2x + p/x²
  3. 3At turning point, dy/dx = 0
  4. 4x = −3, so 2(−3) + p/(−3)² = 0
  5. 5−6 + p/9 = 0
  6. 6p/9 = 6
  7. 7p = 54

Answer54

Part (b) · 3 marks

For y = x² − 16/x, determine k such that the horizontal line y = k is tangent to the curve.

  1. 1y = x² − 16/x
  2. 2dy/dx = 2x + 16/x²
  3. 3Set dy/dx = 0: 2x + 16/x² = 0
  4. 42x = −16/x²
  5. 52x³ = −16
  6. 6x³ = −8
  7. 7x = −2
  8. 8Substitute x = −2 into y = x² − 16/x
  9. 9y = (−2)² − 16/(−2)
  10. 10y = 4 + 8
  11. 11y = 12
  12. 12The tangent line y = k touches at this point, so k = 12

Answer12

Stuck on a step? Read the free lesson: Stationary Points and Turning Points

Practise more stationary points and turning points questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on stationary points and turning points

Also searched as: 4MA1 1HR June 2022 · 4MA1/1HR · 4ma1 jun22 1hr · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.