Find all critical values for the function f(r)=2r/9r^2+6

Assuming you mean

f(r) = 2r/(9r^2+6), then
f'(r) = (4-6r^2) / 3(9r^2+6)^2
Since the bottom is always positive, just find where
4-6r^2 = 0
r = ±√(2/3)