2023 SCSS P2 Q7

2023 SCSS P2 Q7

Secondary 4
9 marks

It is given that \(\mathrm f(x)=\dfrac{5x}{(3x-2)(x+1)}\), where \(x\ne\dfrac23\) and \(x\ne-1\).

  1. Express \(\mathrm f(x)\) in partial fractions.[4]
  2. Hence find \(\mathrm f'(x)\).[3]
  3. Given that a curve has equation \(y=\mathrm f(x)\), explain why the gradient of every point on the curve is negative.[2]

Solution:

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Answer:(i) \(\dfrac2{3x-2}+\dfrac1{x+1}\). (ii) \(-\dfrac6{(3x-2)^2}-\dfrac1{(x+1)^2}\). (iii) Both terms are negative on the domain.

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