In the answer space below, provide one of the two positive integers whose sum is 200 and whose product is a maximum.

Yay for Calculus!
First, use the equation:
xy=S
This is x times y is equal to sum, or S.
Then, use the equation x + y = 200.
Then, solve for x or y. I will solve for y.
Doing so gives me the equation y = 200 - x
Next, use this value for y in the equation xy = S.
Give: x(200-x) = S
Simplify: 200x - x^2 = S.
Take the derivative: 200 - 2x = S'
Set it equal to 0 for critical numbers: 200 - 2x = 0
Solve: -2x = -200
Solve: 2x = 200
Sove: x = 100, which is one of your integers. The other is also 100.

               

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