2026 NASS P2 Q8

2026 NASS P2 Q8

Secondary 4
9 marks

The curve \(C\) has equation \(y=x^3+ax^2+bx+4\), where \(a\) and \(b\) are constants. It is given that \(C\) has a stationary point when \(x=1\). The tangent to \(C\) at \(x=2\) is parallel to the line \(y=-3x+7\).

  1. Find the values of \(a\) and \(b\).[4]
  2. Find the coordinates of all the stationary points of \(C\), and determine their nature.[5]

Solution:

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Answer:(a) \(a=-6,b=9\). (b) Local maximum \((1,8)\); local minimum \((3,4)\).

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