Suppose $x(t) = 2t^{2}$, $y(t) = t^{3}-4t$, and $\vec{r}(t) = \langle x(t), y(t) \rangle$.

(a) Find $\vec{r}^{\,\prime}(t)$ and $\vec{r}^{\,\prime\prime}(t)$.
$\vec{r}^{\,\prime}(t) =$
$\vec{r}^{\,\prime\prime}(t) =$

(b) Find $\displaystyle \frac{dy}{dx}$ and $\displaystyle \frac{d^2y}{dx^2}$ in terms of the parameter $t$ (i.e., without eliminating the parameter $t$) for $t \ne 0$.
$\displaystyle \frac{dy}{dx} =$

$\displaystyle \frac{d^2y}{dx^2} =$