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5 marksDifferentiation

CAPE Integrated Mathematics · 2016 · Paper 2 · Question 5(b)(i)

Given that f(x) = x^3 ln 2x, find f'(x), the first derivative of f(x).

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Other parts of this question

  1. 5(a)(i)Evaluate lim_{x -> 1+} f(x).[2 marks]
  2. 5(a)(ii)Determine whether the function f(x) is continuous at x = 1. Justify your answer.[2 marks]
  3. 5(b)(ii)Determine the derivative of the function g(x) = e^(2x) + cos 3x with respect to x.[3 marks]
  4. 5(c)(i)Find the second derivative, P''(t).[3 marks]
  5. 5(c)(ii)Given that the function P(t) has a stationary point when t = 48, show that the stationary point is a maximum point.[2 marks]
  6. 5(c)(iii)Find the population count when t = 48 days.[3 marks]
  7. 5(d)(i)Obtain an expression for dV/dt.[1 mark]
  8. 5(d)(ii)Find the rate of increase of the volume of the balloon, dV/dt, at the instant when r = 5 cm. Give your answer in terms of pi.[4 marks]

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