A curve is such that $ \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{8}{x^2} - 2$. Given that the c

Question

A curve is such that $ \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{8}{x^2} - 2$. Given that the curve passes through the point $(1, 5)$, find the equation of the curve.[3] Find the $x$-coordinates of the stationary points of the curve.[2] Obtain an expression for $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$ and hence, or otherwise, determine the nature of each stationary point.[3]

Accepted Answer

(a) $y=-8/x-2x+15$ for $x>0$; independent constant for $x<0$. (b) $x=\pm2$. (c) Local maximum at 2; local minimum at $-2$.

2024 FMSS PRELIMS P2 Q6

2024 FMSS PRELIMS P2 Q6

Solution:

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