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A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2021 · Q36 Marks

The curve with equation y = xe¹⁻²ˣ has one stationary point.

  1. (a)Find the coordinates of this point.[4]
  2. (b)Determine whether the stationary point is a maximum or a minimum.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [M1] Use correct product rule
  2. [A1] Obtain correct derivative in any form
  3. [M1] Equate derivative to zero and solve for x
  4. [A1] Obtain x = ½ and y = ½e⁰ = ½
  5. [M1] Use a correct method for determining the nature of a stationary point
  6. [A1] Show that it is a maximum point

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 3 Variant 1, question 3.

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