Let 2 integers that differ by 7 are x , x+7
let the product of the 2 integers that differ by 7 is y
∴ y = x(x+7) = x² + 7x
By graphing y = x² + 7x ⇒⇒⇒ see the attached figure
There is a minimum point at x = -3.5 which give y = -12.25
∵ The product of two integers will be an integer number
So, the nearest integer number to the minimum value = -12
∴ The smallest possible value for the product of 2 integers that differ by 7 is (-12)