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A-LevelFurther MathematicsDifferentiation9231/12 · Oct/Nov 2011 · Q57 Marks

The point P (2, 1) lies on the curve with equation `x³ - 2y³ = 3xy`.

  1. (i)the value of `dy/dx` at P,[3]
  2. (ii)the value of `d²y/dx²` at P.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [B1B1] One mark for each side. 3x² - 6y² y' = 3y + 3xy'
  2. [B1√] Substitutes (2,1) 12 - 6y' = 3 + 6y' ⇒ y' = 3/4
  3. [B1B1B1] One mark for differentiating both 1st and 3rd terms. One mark for each of 2nd and 4th terms. 6x - {6y²y'' + 12y(y')²}=3y' + 3y' + 3xy''
  4. [B1] Substitute (2,1) and y'(2) = 3/4 12 - (6y'' + 27/4) = 3/4 + 3/4 + 6y'' ⇒ 12y'' = -1/16 ⇒ y'' = -1/16

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About this question

Topic
Differentiation, A-Level Further Mathematics (syllabus 9231). Structured question, 7 marks.
Source
A-Level Further Mathematics, Oct/Nov 2011 Paper 1 Variant 2, question 5.

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