1a) Determine the maximum value of f(x,y,z)=(xyz)1/3 given that x,y,z are nonnegative numbers and x+y+z=k, k a constant. 1b) Use the result in (a) to show that if x,y,z are nonnegative numbers, then (xyz)1/3 < (x+y+z)/3 Attempt: 1a) Using the Lagrange Multiplier method, I get that the absolute maximum of f subject to the constraints x+y+z=k and x,y,z>0 is k/3 1b) Here, it seems to me that one of the constraints, namely x+y+z=k, is removed. If so, then how can we still use the result of part (a) here? I need some help on part (b). Any help is appreciated!