2023 ACJC Promo Q4
2023 ACJC Promo Q4
7 marks
Promo
Do not use a calculator in answering this question.
A curve \(C\) has equation \({{y}^{2}}+3xy=13+{{x}^{2}}\).
- Find the coordinates of the stationary points of \(C\).[4]
- For the stationary point with \(x>0\), determine whether it is a maximum or minimum point.[3]
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Answer:(i) \({(3, 2)}\), \({(-3, -2)}\). (ii) \({\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = \frac{2}{13} > 0}\). \({(3, 2)}\) is a minimum point.
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