2026 ZHSS P1 Q9

2026 ZHSS P1 Q9

Secondary 4
6 marks

The curve \(y=\dfrac5{\sqrt x}+x-2\) has a stationary point \(A\) where \(x>0\).

  1. Show that the \(x\)-coordinate of the stationary point \(A\) is \(\sqrt[3]{\dfrac{25}{4}}\).[3]
  2. Determine the nature of the stationary point \(A\).[3]

Solution:

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Answer:(a) \(x=\sqrt[3]{\dfrac{25}{4}}\) (shown) (b) Minimum point

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