Notice that the curve given by the parametric equations $$\begin{array}{r@{\,}c@{\,}l} x & = & 36 - t^2 \cr y & = & t^3 - 4 t \end{array}$$ is symmetric about the $x$-axis. (If $t$ gives us the point $(x,y)$, then $-t$ will give $(x,-y)$ ).
At which $x$ value is the tangent to this curve horizontal?
$x =$ .
At which $t$ value is the tangent to this curve vertical?
$t =$ .
The curve makes a loop which lies along the $x$-axis. What is the total area inside the loop?
${\rm Area} =$ .