- #1

kingwinner

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**1a) Determine the maximum value of f(x,y,z)=(xyz)**

1b) Use the result in (a) to show that if x,y,z are nonnegative numbers, then (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!