Hi natH. The distance from the Origin to a point on the polar curve is r. We're told that r-values are the same as f-values. We're told that t is the same number as θ. Therefore, distance r is a function of time:
r(t) = t^3 - 6t^2 + 9t
Do you know how to use calculus, to find the intervals where distance r(t) is increasing, while 0 ≤ t ≤ 2pi seconds?