Point $P(3, 5)$ belongs to the curve $y = \frac{1}{x - 1} - \frac{9}{x - 5}$.
(i)[5]
Find the $x$-coordinate of the point at which the normal to the curve at $P$ crosses the $x$-axis.
(ii)[6]
Find the $x$-coordinate of each stationary point on the curve and determine the type of each stationary point, with reasons for your answers.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly differentiates to $\frac{dy}{dx}=-(x-1)^{-2}+9(x-5)^{-2}$” …