Which are the two numbers whose sum is 20 and the product is

Which are the two numbers whose sum is 20 and the product is the maximum.

Solution

Let us assume one of the numbers is x. As the sum of the two numbers is 20, the other number is 20-x

The product of the two numbers is a function f(x) = x*(20-x) = 20x- x^2.

Now we need to find the maximum value of f (x). For this we need the derivative of f(x) and have to equate it to 0.

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