In the space below, provide the smaller of the two positive integers that add to 40 and have the largest possible product

Answer 1

same as your fence really
a + b = 40 so b = 40 - a

P = a b = a(40-a) = 40 a - a^2

dP/da = 40 - 2 a
a = 20
then b = 20
so
20 and 20

Answer 2

a + b = 40 so b = 40 - a

P = a b = a(40-a) = 40 a - a^2

dP/da = 40 - 2 a
a = 20
then b = 20
so
20 and 20