Question 504161
If the two numbers are a and b, then a+b = 56 which can be written as a = 56-b.
Now a*b must be a maximum (call it y)so we can write a*b as:
{{{y = (56-b)*b}}} Simplify.
{{{y = 56b-b^2}}} This is a quadratic equation and the graph will be a parabola opening downward.
So all you need to do to find the maximum is find the value of b at the point of the parabola's vertex which is given by:
{{{b = -56/2(-1)}}}
{{{b = 28}}}
So the two numbers are: a = 28 and b = 28.