2024 IGCSE Additional Mathematics October/November 0606/12 Q2

2024 IGCSE Additional Mathematics October/November 0606/12 Q2

9 marks

It is given that \(y=\mathrm{f}(x)\), where \(\mathrm{f}(x)=(2x-5)(x-1)^2\).

  1. Find the coordinates of the stationary points on the curve \(y=\mathrm{f}(x)\).[4]
  2. On the axes, sketch the graph of \(y=\mathrm{f}(x)\), stating the intercepts with the axes.[3]
  3. Hence find the values of \(k\) for which \(\mathrm{f}(x)=k\) has exactly one solution.[2]

Solution:

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Answer:(a) \((1,0),(2,-1)\). (b) Intercepts \((1,0),(\dfrac52,0),(0,-5)\); sketch shown. (c) \(k<-1\) or \(k>0\).

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