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\noindent {\bf Problem statement} A curve is given parametrically by
these equations:

$$x(t) = {\textstyle {1\over 3}}t^3 - 5t\ {\rm and}\ y(t) = t^2 - 2t\, .$$

\noindent a) Sketch $x$ and $y$ as functions of $t$, giving the
intercepts and critical points of each function.

\medskip
 
\noindent b) Sketch the curve and identify the points where the curve
crosses the $x$-axis and the $y$-axis.

\medskip

\noindent c) Locate (exactly!) the points on the curve where the
tangent to the curve is parallel to the $x$-axis, parallel to the
$y$-axis, and parallel to the line $y=x$.









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