$-7,7$, minimum product $-49$
Work Step by Step
Step 1. Assume the lower number is $x$; then the other number is $x+14$. Step 2. Their product is given by $f(x)=x(x+14)=x^2+14x=x^2+14x+49-49=(x+7)^2-49$ Step 3. Thus, the numbers are $-7,7$ and the minimum product is $-49$.