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WMA11/01 Jun 2021, Question 6: Integration: Undoing Differentiation

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Curve C with y = f(x), x > 0, passes through P(8, 2) and has derivative f′(x) = 32/(3x²) + 3 − 2∛x. Find the tangent at P and then f(x).

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

Part (a) · 3 marks

Find the tangent to C at P(8, 2), giving it as y = mx + c with m and c to be found.

  1. 1f′(8) = 32/(3 × 64) + 3 − 2∛8 = 1/6 + 3 − 4 = −5/6
  2. 2y − 2 = −(5/6)(x − 8)
  3. 3y = −(5/6)x + 20/3 + 2
  4. 4y = −(5/6)x + 26/3

Answery = −(5/6)x + 26/3

Part (b) · 5 marks

Find f(x) in simplest form using the given derivative and the point P(8, 2).

  1. 1f′(x) = (32/3)x⁻² + 3 − 2x^(1/3)
  2. 2f(x) = −(32/3)x⁻¹ + 3x − (3/2)x^(4/3) + c
  3. 3At (8, 2): 2 = −32/24 + 24 − (3/2)(16) + c
  4. 42 = −4/3 + 24 − 24 + c, so c = 10/3
  5. 5f(x) = −32/(3x) + 3x − (3/2)x^(4/3) + 10/3

Answerf(x) = −32/(3x) + 3x − (3/2)x^(4/3) + 10/3

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