Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞(a) Find all t that give x intercepts and y-intercepts, and plotthem.
(b) Find all t which give horizontal or vertical tangents, andplot the corresponding points, with a short horizontal or verticalsegment to indicate the tangent line.
(c) Find the values of t for which x(t) is increasing and thosefor which it is decreasing. Do the same for y.
(d) Determine what happens to x(t) and y(t) as t → ∞.
(e) Make a neat, careful sketch of the graph on the axes above.Use arrows which indicate the direction, and label all importantvalues of t. Your graph must be consistent with the information inparts (a)-(d).
