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True.
True
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Let the sum of series a1,.., an = A. Since ai >0. Then the maximum possible product of a1,..,an is = (A/n)n. This result basically comes the relation between the arithmetic mean and geometric mean of n positive numbers. A/n >= (a1...an)(1/n). The equality case of the above relation gives the maximum product (by raising the power by n on both sides).
It has an absolute minimum at the point (2,3). It has no maximum but the ends of the graph both approach infinity.