The sum of 2 numbers is 18. What is their maximum product.

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The sum of two numbers is 18. If one of the numbers is x, the other number is 18 - x.

The product of the two numbers is P = x*(18 - x) = 18x - x^2

To determine the maximum value of P, solve P' = 0 for x.

P' = 18 - 2x

P' = 0

=> 18 - 2x = 0

=> x = 9

This gives the other number as 9 too, the product of the two is 9*9 = 81

The maximum value of the product of the numbers is 81.

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