the sum of two numbers is fixed. Then its multiplication is maximum, when

Options

A. each number is half of the sum
B. each number is `(1)/(3)` and `(2)/(3)` respectively of the sum
C. each number is `(1)/(4)` and `(3)/(4)` respectively of the sum
D. none of these

Answer

A

Explanation

Suppose that two numbers are x and y.
`x+y=simpliesy=s-x`
Then `f(x)=xy=x(s-x)=xs-x^(2)`
`becausef^(`)(x)=s-2x`
`f^(`)(x)=0` for maximum value of `f(x)`
`x=(s)/(2)` and `y=(s)/(2)`
Thus each number is half of the sum.