Suppose $x(t) = 2t^{2}$ and $y(t) = t^{3}-4t$.

(a) Find $x^{\,\prime}(t)$ and $y^{\,\prime}(t)$.

$x^{\,\prime}(t)$	=
$y^{\,\prime}(t)$	=

(b) Use $x^{\,\prime}(t)$ and $y^{\,\prime}(t)$ to determine when $x(t)$ and $y(t)$ are increasing and decreasing. Then, find the intervals of $t$ for which the motion of the curve is up, down, right, and left in the $xy$-plane. (Your answers below should be intervals of $t$ values.)

Up and to the right:
Up and to the left:
Down and to the right:
Down and to the left: