Question 1191565
Find two nonnegative numbers whose sum is 12 such that their product is an absolute maximum.
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6 and 6.
It's always equal numbers
In this case, the product is 36.
x*x = 36 is the max and x+x = 12
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Any other combination is less than 36
(x-1)*(x+1) = x^2 - 1 = 35
(x-2)*(x+2) = x^2 - 4 = 32
(x-k)*(x+k) = x^2 - k^2 = 36 - k^2