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A-LevelMathematicsDifferentiation9709/33 · May/June 2024 · Q25 Marks

Find the exact coordinates of the stationary point of the curve y = e²ˣ sin2x for 0 ≤ x ≤ ½π.

  1. Find the exact coordinates of the stationary point of the curve y = e²ˣ sin2x for 0 ≤ x ≤ ½π.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] Use correct product rule
  2. [A1] Obtain correct derivative 2e²ˣsin2x + 2e²ˣcos2x
  3. [M1] Equate derivative of the form ae²ˣsin2x + e²ˣbcos2x to 0 and solve for 2x or x using a correct method
  4. [A1] Obtain x = ¾π only or exact equivalent
  5. [A1] Obtain y = - (1/√2)e^(3π/2) only or exact simplified equivalent

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2024 Paper 3 Variant 3, question 2.

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