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4 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 5(c)(ii)

A farmer plans to construct an enclosure for his sheep, using one side of a barn 150 m long. With 500 m of fencing, a fence QRSTP will be built to form a rectangular enclosure PRST with the barn wall PQ. The length of QR is x metres.

Simplifying your answers where possible, find expressions in terms of x for the length of RS.

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Other parts of this question

  1. 5(a)Using differentiation, determine the range of real values of x for which the function f: x → 12 + 6x² - x³ is decreasing.[5 marks]
  2. 5(b)Differentiate x³ with respect to x from first principles.[6 marks]
  3. 5(c)(i)Simplifying your answers where possible, find expressions in terms of x for the length of TS.[1 mark]
  4. 5(c)(iii)Simplifying your answers where possible, find expressions in terms of x for the area, A, of PRST.[2 marks]
  5. 5(c)(iv)Simplifying your answers where possible, find expressions in terms of x for the stationary value of x and show that it is a maximum.[5 marks]
  6. 5(c)(v)Simplifying your answers where possible, find expressions in terms of x for the maximum area of the sheep enclosure.[2 marks]

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