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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 2 · Question 5(d)

The function f(x) is such that f'(x) = 3x² + 6x + k where k is a constant. Given that f(0) = -6 and f(1) = -3.

Find the function f(x).

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Other parts of this question

  1. 5(a)Find lim (x³ - 8) / (x² - 6x + 8) as x → 2.[5 marks]
  2. 5(b)(i)Sketch the graph of f(x) for the domain -1 ≤ x ≤ 2.[2 marks]
  3. 5(b)(ii)a)Find lim f(x) as x → 1+.[2 marks]
  4. 5(b)(ii)b)Find lim f(x) as x → 1-.[2 marks]
  5. 5(b)(iii)Deduce that f(x) is continuous at x = 1.[3 marks]
  6. 5(c)Differentiate from first principles, with respect to x, the function y = 1/x².[6 marks]

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