Question 2620: find two numbers whose sum is 50and whose product is a maximum
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Let x be one of them,another is 50-x,
their product f(x) = x(50-x) = -(x^2-50x+(50/2)^2) +625
= 625 -(x-25)^2 [Use complete square]
Since -(x-25)^2 <=0, f(x) <= 625.
when x = 25, f(x) has max value 625.
Thus, when the two numbers are 25, 25(in fact equal), their
procudt is max(vale 625).
Kenny
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