Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve $C$ is given by the equation $y = \frac{9}{2x - 5} + 2x - 5$.
(a)[4]

Determine the coordinates of the two stationary points.

(b)[3]

Find $\frac{d^2 y}{dx^2}$ and so determine the nature of each stationary point.

(c(i))[1]

The curve $C$ is mapped to the curve $C_1$ by a translation of $\begin{pmatrix} -3 \\ 7 \end{pmatrix}$ followed by reflection in the $x$-axis. State the coordinates of the maximum point of $C_1$.

(c(ii))[3]

Find the equation of $C_1$ in the form $y = \frac{a}{bx + c} + dx + e$, where $a$, $b$, $c$, $d$ and $e$ are integers.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correctly differentiated to $-18(2x-5)^{-2}+2$

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