Question

Find two positive real numbers whose product is a maximum. The sum is 10.

Answer 1

call then x and y, so you have:
x + y = 10
y = 10 -x

we can then write the product as:
p = xy = x(10-x) = 10x - x^2

differentiate and set to zero to find what value of x gives the max.
have you done differentials?