Let's call x and y to the unknown numbers. Their addition must be equal to 221, then:
x + y = 221
Isolating y, we get:
y = 221 - x
The product of these numbers is:
[tex]\begin{gathered} f(x)=x\cdot y \\ f(x)=x(221-x) \\ \text{ Distributing:} \\ f(x)=221x-x^2 \\ Or \\ f\mleft(x\mright)=-x^2+221x \end{gathered}[/tex]In this function, the leading coefficient is negative (-1), then the quadratic function has a maximum.