2022 BTYSS P2 Q5

2022 BTYSS P2 Q5

Secondary 4
9 marks

The point \((-3,0)\) is a stationary point on the graph of \(y=x^3+hx^2+3x+k\).

  1. Show that \(h=5\).[3]
  2. Find the value of \(k\).[1]
  3. Find the \(x\)-coordinate of the other stationary point.[2]
  4. Determine the nature of each of these stationary points.[3]

Solution:

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Answer:(a) \(h=5\). (b) \(k=-9\). (c) \(x=-\dfrac13\). (d) Maximum at \(x=-3\); minimum at \(x=-\dfrac13\).

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