Answer
a. see graph; increases on $(0,3\pi)$; decreases on $(3\pi,6\pi)$
b. maximum at $(3\pi,6)$; minima at $(0,0)$ and $(6\pi,0)$
Work Step by Step
a. Using various $t$ values in $[0,2\pi]$, we can graph the plane curve as shown in the figure. We can identify that the function increases over $(0,3\pi)$ and decreases over $(3\pi,6\pi)$.
b. We can find a maximum at $(3\pi,6)$ and minima at $(0,0)$ and $(6\pi,0)$.
