2026 ZHSS P2 Q8

2026 ZHSS P2 Q8

Secondary 4
8 marks
  1. Given that \(y=\dfrac{x^2-4x+3}{(x-2)^2}\), show that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac2{(x-2)^3}\).[3]
  2. Find the range of values that the curve \(y=\dfrac{x^2-4x+3}{(x-2)^2}\) is increasing.[2]
  3. Hence, determine whether the gradient of the curve \(y=\dfrac{x^2-4x+3}{(x-2)^2}\) is increasing or decreasing for \(x\ne2\).[3]

Solution:

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Answer:(a) \(y'=\dfrac2{(x-2)^3}\) (shown) (b) \(x>2\) (c) The gradient decreases on each interval \(( -\infty,2)\) and \((2,\infty)\).

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