$7(e)$ should ask for the point $of$ self$-$intersection from part $(d).$ Answer the questions about the parametric curve given $by$

$t(x,y)xyxy(x,y)tt(x,y)x(t)=t^2-2t,y(t)=t^3+t^2-6t,-$

For any questions asking where the curve has a certain property, give both the value$(s)$

$oft$ and the $(x,y)$ coordinates

$(a)(5$ points$)$ Write the equation for the curve $in$ the variables $x$ and $y.Itis$ not $a$

function $ofxory.$

$(b)(3$ points$)$ Find all critical points $(give(x,y)$ coordinates, not just values $oft)$ and

indicate $if$ the tangent line $at$ each point $is$ vertical $or$ horizontal.

$(c)(3$ points$)$ Where does the concavity change? Where $is$ the curve concave $up?$

$(d)(4$ points$)$ Give both the values $oft$ and the $(x,y)$ coordinate $of$ a point $on$ the curve

where $it$ self$-$intersects. Find the equations for both tangent lines $at$ this point

$(e)(3$ points$)$ For the point $of$ self$-$intersection from part $(b),$ set $up,$ but $do$ not evalu$-$

ate, the integral for computing the distance traveled $by$ the curve between the first

time $it$ goes through this point and the second time.