Problem

A curve $C$ has equation $y = \frac{9}{2x - 5} + 2x - 5$.

(a) Find the coordinates of the two stationary points.

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

(c) The curve $C$ is transformed to the curve $C_1$ using a translation of $\begin{pmatrix}-3\\7\end{pmatrix}$ followed by reflection in the $x$-axis.

(i) State the coordinates of the maximum point of $C_1$.

(ii) 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.