Word Problems Involving Quadratic Functions

Let x be the first number and let(4-x) be the second number.

And call their product "P"

So

P = x (4-x)

P = 4x - x²     take the derivative (P') and set this to 0   ... so we have

4 - 2x = 0      add 2x to both sides

4 = 2x           divide both sides by 2

2 = x            

And the second number  is (4-x)  = (4-2)   = 2

So....x = y = 2