2023 SCSS P1 Q4

2023 SCSS P1 Q4

Secondary 4
6 marks

A curve has gradient \(2(x^2+3)\) at every point on the curve. It is given that the curve passes through the point \((1,12)\).

  1. Find the equation of the curve.[4]
  2. Explain why this curve has no stationary point.[1]
  3. Given that the equation of the curve can be written in the form \(y=\mathrm P(x)\), explain why \(\mathrm P(x)\) is an increasing function.[1]

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Answer:(i) \(y=\dfrac23x^3+6x+\dfrac{16}3\). (ii) Derivative never zero. (iii) Derivative always positive.

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