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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2017 · Q78 Marks

Show that the curve y = (3x² + 8)² has only one stationary point. Find the coordinates of this stationary point and determine its nature.

  1. Show that the curve y = (3x² + 8)² has only one stationary point. Find the coordinates of this stationary point and determine its nature.[8]

Mark scheme

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

  1. [M1] differentiation to obtain answer in the form p(3x² +8) or qx(3x² +8)
  2. [B1] 6x(3x² +8)
  3. [A1] dy/dx = 12x(3x² +8) all correct
  4. [DM1] When dy/dx = 0 only solution is x = 0 qx(3x² +8) = 0 and attempt to solve
  5. [A1] x=0 and 3x² +8 = 0 has no solutions
  6. [A1] Stationary point at (0,32)
  7. [M1] correct gradient method with substitution of x values either side of zero or equivalent valid method
  8. [A1] correct conclusion from correct work using a correct dy/dx

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2017 Paper 1 Variant 1, question 7.

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