Question

Find two numbers whose difference is 108 and whose product is a minimum. (smaller number) (larger number)

Answer 1

Let
x---------------> smaller number
y----------------> larger number

we know that
y-x=108---------> y=108+x

product------------> x*y-------> x*(108+x)-----> 108x+x²

find the derivative and equals to zero
dx/dy=108+2x-------------> 108+2x=0---------> 2x=-108--------> x=-54

then
y=108+x-------> y=108-54-----> y=54

the answer is
smaller number is -54
larger number is 54