O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2020 · Q710 Marks

Given that y = (x²-1)√5x+2, show that dy/dx = (Ax²+Bx+C) / (2√5x+2) where A, B and C are integers.

(a)Given that y = (x²-1)√5x+2, show that dy/dx = (Ax²+Bx+C) / (2√5x+2) where A, B and C are integers.[5]
(b)Find the coordinates of the stationary point of the curve y = (x²-1)√5x+2, for x > 0. Give each coordinate correct to 2 significant figures.[3]
(c)Determine the nature of this stationary point.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[1] For (5/2)(5x+2)^(1/2)
[1] For differentiation of a product
[1]
[1] Dep on previous M mark for attempt to simplify
[1] dy/dx = (25x²+8x-5) / (2√5x+2)
[1] Equating their numerator in (a) to zero and attempt to solve
[1] x = 0.315
[1] y = -1.70
[1] Consideration of gradient or y values either side of stationary point, remembering that x > 0. Must be a complete method making use of their (a). Allow consideration of 25x² + 8x – 5 as a ‘minimum curve’. Accept 2nd derivative method.
[1] Minimum

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source: O-Level Additional Mathematics, May/June 2020 Paper 1 Variant 2, question 7.

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