Let one number be x, then the other is (76 - x)

Product = x*(76 - x) = -x^2 + 76*x

For the product to be maximum, its first derivative should be 0, and the second
derivative should be negative.

First derivative = -2*x + 76 = 0
i.e 2*x = 76
x = 38

Second derivative = -2, which is negative, so it is a maximum value.

So the 2 numbers are 38 and 38 to get the maximum product.

:)