My directions for this problem are to find the power delivered when RL=3 and then find the maximum power.
I found Rth = R1//R2 = 1 Ohm. Then I used Vth=InRth to find that Vth = 6V.
After doing this, I used P=RL*(Vth/(Rth+RL))^2 to get P=27W when RL=3.
From here I set RL=Rth to find the maximum power, then used Pmax=Rth*(Vth/2Rth)^2 to find that Pmax= 9W.
I know this can't be right since the maximum power is less than the power I found before, but I'm not sure where I'm going wrong.