0606/12 Feb/Mar 2026, Question 7: Connected Rates of Change and Small Changes
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Given y = 3√x + 1/√x, use calculus to estimate how y changes when x moves from 4 to 4 + h for small h.
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Solution · 4 marks
- 1y = 3x^(1/2) + x^(−1/2)
- 2dy/dx = (3/2)x^(−1/2) − (1/2)x^(−3/2)
- 3At x = 4: dy/dx = (3/2)(1/2) − (1/2)(1/8) = 3/4 − 1/16 = 11/16
- 4δy ≈ (dy/dx)h = (11/16)h
Answer(11/16)h
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