Answer
$49$
Work Step by Step
Let one of the numbers be $x$, then the other one is $14-x$, then their product is $x(14-x)=-x^2+14x$
The maximum value is at $x=-\frac{b}{2a}=-\frac{14}{2\cdot(-1)}=7.$ Hence the maximum value is $f(7)=-(7)^2+14(7)=49.$
