Find two positive numbers that satisfy the given requirements.

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Find two positive numbers that satisfy the given requirements.

The sum is S and the product is a maximum

smaller value?

larger value ?

Answer 1

Let the numbers are x and y.

Sum, s = x + y

y = s - x

Product, P = xy

P = x (s - x)

   = sx - x^2

Product is maximum:

dP/dx = 0

s - 2x = 0

x = s/2

y = s - x

   = s - (s/2)

   =s/2