(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.