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3 marksDifferentiation I

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 5(b)(i)

A curve, C, is described parametrically by the equations x = 5t + 3 and y = t² – t + 2.

Find dy/dx in terms of t.

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Other parts of this question

  1. 5(a)Determine the value of k for which f(x) = (x²-1)/(x-1) for x ≠ 1 and f(x) = k for x = 1 is continuous for all values of x.[4 marks]
  2. 5(b)(ii)Hence, determine all points of C such that dy/dx = 0.[6 marks]
  3. 5(c)(i)(a)Show that y(dy/dx) - 2x = 0.[9 marks]
  4. 5(c)(i)(b)Show that d²y/dx² - 4/y³ = 0.[9 marks]
  5. 5(c)(ii)Hence, find the value of d²y/dx² when x = 0.[3 marks]

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