$\mathrm{If} \mathrm{x} = \mathrm{ct}, \mathrm{y} = \mathrm{c}/\mathrm{t}, \mathrm{then} {\mathrm{y}}_2 \mathrm{at} \mathrm{t} = 1/2 \mathrm{is}$

$$\begin{gathered} \mathrm{x}=\mathrm{ct}, \mathrm{y}=\raisebox{1ex}{$\mathrm{c}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{t}$}\right. \\ \frac{\mathrm{dx}}{\mathrm{dy}}=\mathrm{c}, \frac{\mathrm{dy}}{\mathrm{dt}}=\raisebox{1ex}{$-\mathrm{c}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{t}}^2$}\right. \\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\displaystyle \raisebox{1ex}{$\mathrm{dy}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{dt}$}\right.}}{{\displaystyle \raisebox{1ex}{$\mathrm{dx}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{dt}$}\right.}}=\frac{{\displaystyle \raisebox{1ex}{$-\mathrm{c}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{t}}^2$}\right.}}{\mathrm{c}} \\ =\frac{-1}{{\mathrm{t}}^2} \\ \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}=\frac{2}{{\mathrm{t}}^3}·\frac{\mathrm{dt}}{\mathrm{dx}} \\ =\frac{2}{{\mathrm{t}}^3}·\frac{1}{\mathrm{c}} \\ \mathrm{At} \mathrm{t}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \Rightarrow \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}=\frac{16}{\mathrm{c}} \end{gathered}$$