provide one of the two positive integers whose sum is 200 and whose product is a maximum.

Thank you!

You're welcome.

how about 100 and 100

99*101 = 9999
100*100 = 10,000

To find the two positive integers that have a sum of 200 and their product is the maximum, we can use calculus. Let's define the two positive integers as x and y.

Given that x + y = 200, we need to express the product of x and y in terms of a single variable to apply calculus. We can rewrite y as 200 - x.

The product of x and y, denoted as P, can be expressed as:

P = x * (200 - x)

To find the maximum value of P, we need to find the critical points of the function P(x) by taking its derivative and setting it equal to zero:

P'(x) = 200 - 2x = 0

Solving the equation, we get:

200 - 2x = 0
2x = 200
x = 100

So, x = 100 is the critical point. By substituting the value of x back into the equation x + y = 200, we can find y:

100 + y = 200
y = 100

Therefore, the two positive integers that give the maximum product and have a sum of 200 are 100 and 100.

99 and 101