2025 JVSS PRELIMS P1 Q5

2025 JVSS PRELIMS P1 Q5

Secondary 4
6 marks
2025 Jurongville Secondary School Prelims A Math Paper 1

The function \(f\) is defined for \(x>0\) by \(f(x)=\dfrac{x^2+4}{x+1}\).

  1. Find \(f'(x)\) in the form \(\dfrac{ax^2+bx+c}{(x+1)^2}\).[2]
  2. Hence determine the values of \(x\) for which \(f\) is increasing.[4]

Solution:

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Answer:(a) \(f'(x)=\dfrac{x^2+2x-4}{(x+1)^2}\) (b) \(x>\sqrt5-1\)

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