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5 marksDifferentiation II

CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2 · Question 1(a)(i)

Given f(x) = x^3 ln^2 x.

Show that f'(x) = x^2 ln x (3 ln x + 2).

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Other parts of this question

  1. 1(a)(ii)Show that f''(x) = 6x ln^2 x + 10x ln x + 2x.[5 marks]
  2. 1(b)(i)What is the LARGEST number reached by the membership of the club?[2 marks]
  3. 1(b)(ii)Calculate the EXACT value of k and of r.[6 marks]
  4. 1(b)(iii)How many members will there be in the club 3 years after its formation?[2 marks]

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