2025 PHS P1 Q11

2025 PHS P1 Q11

Secondary 4
9 marks

A curve is such that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=12(a+bx)^2\), where \(a\) and \(b\) are integers.

  1. In the case where the curve has a stationary value at \((3,2)\),
    1. find an equation connecting \(a\) and \(b\),[2]
    2. find a possible equation of the curve.[5]
  2. In the case where \(a=1\) and \(b=-1\), determine the nature of the stationary point of the curve.[2]

Solution:

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Answer:(a)(i) \(a+3b=0\). (ii) For example, \(y=4(x-3)^3+2\). (b) Stationary point of inflection at \(x=1\).

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