2025 ESSS P2 Q4

2025 ESSS P2 Q4

Secondary 4
9 marks

A cubic curve has stationary points at \((-2,-3)\) and \((2,a)\), where \(a\) is a constant.

  1. Explain why \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=k(x^2-4)\), where \(k\) is a constant.[2]
  2. Given that the curve passes through \((-1,2)\), determine its equation.[6]
  1. Find the value of \(a\).[1]

Solution:

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Answer:(a) Derivative roots \(\pm2\) give \(k(x^2-4)\). (b) \(y=-x^3+12x+13\). (iii) \(a=29\).

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