0606/12 May/Jun 2026, Question 8: Connected Rates of Change and Small Changes
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
Given y = (5x + 1)/(x − 2), use calculus to find how much x changes when y rises from 4 by a small amount h.
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Solution · 5 marks
- 1dy/dx = (5(x − 2) − (5x + 1))/(x − 2)² = −11/(x − 2)²
- 2When y = 4: 5x + 1 = 4(x − 2), so x = −9
- 3dy/dx = −11/(−11)² = −1/11
- 4δx ≈ δy ÷ (dy/dx) = h ÷ (−1/11)
- 5δx ≈ −11h
Answer−11h
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