Answer
5.5 and 5.5
Work Step by Step
The two numbers are $x$ and $11-x$. The product is $(x)(11-x)$, and we want this to be as large as possible. This product is as large as possible as the vertex.
$x*(11-x)$
$11x-x^2$
$y=-x^2+11x$
$a=-1$, $b=11$, $c=0$
Vertex: $x=-b/2a$
$x=-11/2*-1$
$x=-11/-2$
$x=5.5$
$x*(11-x)$
$5.5*(11-5.5)$
$5.5*5.5$
$30.25$
5.5 and 5.5
