Question

Find the minimum product of two numbers whose difference is 12.
x-y=12

Answer 1

Let x and y be the numbers.
x-y=12
Product = xy = x(12-x) =12x-x^2
P=12x-x^2
dP/dx = 12-2x=0
2x=12
x=6
6-y=12
y=-6

minimum product = -36
Difference = 6-(-6)=12
The numbers are 6 and -6

Answer 2

thanks alot!