Question

Among all pairs of numbers with a sum of 39, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms

Answer 1

39/2, 39/2 give a maximum product.

Explanation:

Let 1 number be x then the other is 39-x.

Product P = x(39 - x)

= 39x - x^2.

Finding the derivative:

dP/dx = 39 - 2x

When P is a maximum or minimum dP/dx = 0, so

39 - 2x = 0

x = 39/2.

The 2 numbers are both 39/2.