the sum of two positive whole numbers is 56. find both if their product is maximum?

Answer 1

The easy way is to note that both numbers have to be equal so 56/2=28


the hard calculus way is to maximize xy given that y=56-x
x+y=56 implies
xy=x(56-x)=56x-x^2= to find maximum of 56x-x^2
differentiating with respect to x gives 56-2x. The critical point is when 56-2x=0 so x=28.y=28

Answer 2

Let x,y be the 2 numbers.
SO, x+y=56.
You want to maximize xy.
So, x=56-y, so maximize (56-y)y=56y-y^2.
Differiniate it, giving you 56-2y.
Set that to 0, or 56-2y=0, so y=28,and so x=28.

Answer 3

28 and 28

Answer 4

3 and 53