(a) Find x '(t) and y'(t). x '(t)= y'(t)= (b) Use x '(t) and y' (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...

X(t)=4t^2 Y(t)=t^3 - 8t

Extracted text: (a) Find x '(t) and y'(t). x '(t)= y'(t)= (b) Use x '(t) and y' (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: