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WMA11/01 Jan 2024, Question 3: Differentiating Roots and Fractional Powers

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

For the curve y = (5x³ − 8)/(2x²) with x > 0, find the derivative in simplest form, then find the tangent at P(2, 4) in the form ax + by + c = 0 with integer coefficients.

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Part (a) · 4 marks

Differentiate y = (5x³ − 8)/(2x²) and simplify the resulting expression fully.

  1. 1y = 5x³/(2x²) − 8/(2x²) = (5/2)x − 4x⁻²
  2. 2dy/dx = 5/2 + 8x⁻³
  3. 3dy/dx = 5/2 + 8/x³

Answerdy/dx = 5/2 + 8/x³

Part (b) · 3 marks

Using P(2, 4) on the curve, find the tangent line there and express it as ax + by + c = 0 with integers a, b, c.

  1. 1At x = 2: dy/dx = 5/2 + 8/8 = 7/2
  2. 2y − 4 = (7/2)(x − 2)
  3. 32y − 8 = 7x − 14
  4. 47x − 2y − 6 = 0

Answer7x − 2y − 6 = 0

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