The point $P$ travels along the curve $C$ with equation $2xy+x-9y=0$. Without expressing $y$ in term

Question

The point $P$ travels along the curve $C$ with equation $2xy+x-9y=0$. Without expressing $y$ in terms of $x$, find an expression for the gradient of the tangent at $P$ in terms of $x$ and $y$. [2] The $x$-coordinate of $P$ is increasing at the rate of $0.02$ units per second when $x=3$. Determine the rate at which the gradient is changing at this instant. [4]

Accepted Answer

(i) $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{2y+1}{9-2x}$; (ii) $\frac{2}{75}$ units/s

2023 SAJC P2 Q4

2023 SAJC P2 Q4

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