0606/12 May/Jun 2025, Question 12: Integrating eˣ, Trig and (ax+b)ⁿ
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Given the gradient (5x − 2)^(1/3) and the curve passing through (2, 32/5), find the coordinates of the stationary point.
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Solution · 6 marks
- 1dy/dx = 0 when 5x − 2 = 0, so x = 2/5
- 2y = ∫ (5x − 2)^(1/3) dx = (3/20)(5x − 2)^(4/3) + c
- 3At (2, 32/5): 32/5 = (3/20)(8)^(4/3) + c = (3/20)(16) + c = 12/5 + c
- 4c = 4
- 5At x = 2/5: y = 0 + 4 = 4, so the stationary point is (2/5, 4)
Answer(2/5, 4)
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