What is the largest possible product you can form from two non-negative numbers whose sum is 46?

Question

What is the largest possible product you can form from two non-negative numbers whose sum is 46? 

Answer 1

Y = 46 - x

P(x) = x(46-x) = 46x - x^2

0= dP/dx = P'(x) = 46 - 2x

x = 23

x=y=23 ---> 569

Answer 2

x + y =46 => y = 46 -x

Product= x(46-x) = 46x - x²

The maximum product occurs when the derivative = 0, i.e. 46 - 2x = 0

Therefore x = 23 and y = 23.