1. The problem statement, all variables and given/known data If x + y = 60 and x,y >0 find greatest value of x( y-30)^2 2. Relevant equations 3. The attempt at a solution I did this by the usual method that is by substituting 60 - x for y and then differentiating the function and equating derivative to zero. I got x = 10 and x=30. At x=30 value is zero and at x=10 value is 4000 so my answer was 4000 But i checked the solution it says that greatest value does not exist It gave the hint that limit x-->60(-) f(x) = 54000 so greatest value does not exist I'm lost here because the fucntion ought to have some greatest value. Help!