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4MA1/1HR Jun 2020, Question 13: Gradient of a Curve at a Point

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks

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The question, in short

Curve C is y = 5x³ − x² − 6x + 4. Find the derivative, then find the x coordinates of the two points where the gradient equals 2, showing algebraic working.

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

Part (a) · 2 marks

Differentiate y = 5x³ − x² − 6x + 4 to find dy/dx.

  1. 1Differentiate 5x³ to get 15x²
  2. 2Differentiate −x² to get −2x
  3. 3Differentiate −6x to get −6
  4. 4So dy/dx = 15x² − 2x − 6

Answer15x² − 2x − 6

Part (b) · 4 marks

Set the gradient equal to 2 and solve to find the x coordinate of each of the two points, showing working.

  1. 1Set 15x² − 2x − 6 = 2
  2. 2Rearrange to 15x² − 2x − 8 = 0
  3. 3Factorise: (3x + 2)(5x − 4) = 0
  4. 4Solve: 3x + 2 = 0 → x = −2/3
  5. 5Solve: 5x − 4 = 0 → x = 4/5
  6. 6So x = −2/3, 4/5

Answer−2/3, 4/5

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