Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

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 $\frac{dy}{dx}=-(x-1)^{-2}+9(x-5)^{-2}$

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