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WMA11/01 Jan 2021, Question 7: The Derivative as a Limit

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Given f(x) = 2x − 3√x − 5 for x > 0, solve two equations, showing full working without calculator methods.

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

Part (a) · 4 marks

Solve f(x) = 9, showing all stages of working.

  1. 12x − 3√x − 5 = 9, so 2x − 3√x − 14 = 0
  2. 2Treat as a quadratic in √x: (2√x − 7)(√x + 2) = 0
  3. 3√x = 7/2 (√x = −2 is impossible)
  4. 4x = (7/2)² = 49/4

Answerx = 49/4

Part (b) · 5 marks

Solve f″(x) = 6, showing all stages of working.

  1. 1f′(x) = 2 − (3/2)x⁻¹ᐟ²
  2. 2f″(x) = (3/4)x⁻³ᐟ²
  3. 3(3/4)x⁻³ᐟ² = 6, so x⁻³ᐟ² = 8
  4. 4x³ᐟ² = 1/8, so x = (1/8)²ᐟ³
  5. 5x = 1/4

Answerx = 1/4

Stuck on a step? Read the free lesson: The Derivative as a Limit

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Also searched as: WMA11 January 2021 · WMA11/01 · wma11 jan21 · IAS Maths Pure Mathematics 1 January 2021 · question 7.
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