(b) You want to maximize .
See signs analysis.
The maximum y occurs when t = 1, because y changes from increasing to
decreasing there.
(c) Since x(1) = 4arctan 1 = π and , the coordinates of the
highest point are (π,6).
Since and , so v(1) = 2,0. This vector is shown on
the graph.
(d) arctan , and . Thus the particle
approaches the point (2π,0).
(a) To find the smallest rectangle with sides parallel to the x- and y-axes,
you need a rectangle formed by vertical and horizontal tangents as shown
in the figure. The vertical tangents are at the x-intercepts, x = ±3. The
