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5 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2007 · Paper 2 · Question 5(b)(iii)

At a certain port, high tides and low tides occur daily. Suppose t minutes after high tide, the height, h metres, of the tide above a fixed point is given by h = 2(1 + cos(πt/450)), 0 ≤ t. Note: High tide occurs when h has its maximum value and low tide when h has its minimum value.

Determine the rate, in metres per minute, at which the tide is falling 75 minutes after high tide.

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Other parts of this question

  1. 5(a)(i)Obtain dy/dx.[4 marks]
  2. 5(a)(ii)Show that y dy/dx = 5x.[2 marks]
  3. 5(a)(iii)Hence, or otherwise, show that y d^2y/dx^2 + (dy/dx)^2 = 5.[4 marks]
  4. 5(b)(i)Determine the height of the tide when high tide occurs for the first time.[2 marks]
  5. 5(b)(ii)Determine the length of time which elapses between the first high tide and the first low tide.[3 marks]

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