There are no numbers that give the least product.
Let [tex]a[/tex] and [tex]b[/tex] be the two numbers. The sum, therefore, is represented by the equation;
[tex]a+b=7[/tex]
Solving for [tex]b[/tex], we have [tex]b=7-a[/tex]. Substituting
[tex]ab=a(7-a)=-a^2+7a[/tex]
The leading coefficient is negative so the graph of the function is a downward parabola (see attached file).
Notice that the parabola extends downward forever to [tex]-\infty[/tex], therefore, the parabola does not have a minimum point.
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