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A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2017 · Q58 Marks

The equation of a curve is 2x⁴ + xy³ + y⁴ = 10.

  1. (i)Show that dy/dx = - (8x³ + y³) / (3xy² + 4y³)[4]
  2. (ii)Hence show that there are two points on the curve at which the tangent is parallel to the x-axis and find the coordinates of these points.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] (i) State or imply y³ + 3xy² dy/dx as derivative of xy³
  2. [B1] (i) State or imply 4y³ dy/dx as derivative of y⁴
  3. [M1] (i) Equate derivative of the LHS to zero and solve for dy/dx
  4. [A1] (i) Obtain the given answer
  5. [*M1] (ii) Equate numerator to zero
  6. [A1] (ii) Obtain y = -2x, or equivalent
  7. [DM1] (ii) Obtain an equation in x or y
  8. [A1] (ii) Obtain final answer x = −1, y = 2 and x = 1, y = −2

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2017 Paper 3 Variant 1, question 5.

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