Find two numbers A and B (with A≤B) whose difference is 36 and whose product is minimized.

B-A=36

AB=max

B-A=36

add A to both sides

B=36+A

sub that for B in other equation

A (36+A) = max

distribute

A²+36A=max

take derivitive

2A+36=max'

set to zero to find A value

2A+36=0

2A=-36

A=-18

sub back

B=36+A

B=36-18

B=18

de numbers are - 18 and 18

the product is 324