The curve $C$ has parametric equations

$$x = t ^ { 2 } , \quad y = ( 2 - t ) ^ { \frac { 1 } { 2 } } , \quad \text { for } 0 \leqslant t \leqslant 2 .$$

Find\\
(i) $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ in terms of $t$,\\
(ii) the mean value of $y$ with respect to $x$ over the interval $0 \leqslant x \leqslant 4$,\\
(iii) the $y$-coordinate of the centroid of the region enclosed by $C$, the $x$-axis and the $y$-axis.

\hfill \mbox{\textit{CAIE FP1 2014 Q12 EITHER}}