Hey guys, Im currently struggling with this HW question. I was really confused by the condition that f '(x) > 0 for all x > 0, since I thought I need to set f '(..) to zero for maximizing the utility function.

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Calculate the consumer's system of demand funcations D1(P1, P2, I) and D2(P1, P2, I) if the consumer's utility functions is defined by:

U(X1, X2) = f [X1^(1/2) * X2^(1/2)]

where f is a continuously differentiable function of one variable which has f '(x) > 0 for all x > 0.

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Thank you very much in advance!