- #1

Elias Waranoi

- 45

- 2

## Homework Statement

Verify that the sum of three quantities x, y, z, whose product is a constant k, is maximum when these three quantities are equal.

## Homework Equations

w = x + y + z

k = x * y * z

## The Attempt at a Solution

Assuming that my understanding of the question is correct i.e. that we want the maximum of w and x*y*z has to be equal to a constant k then I'm pretty lost. If they mean the maximum as the largest value of w possible then it's definitely not when x = y = z.

If k = 1 then if x = y = z would give w = 3. But if k = 1 and x = 100, y = 0.1, z = 0.1 then k is still 1 and w = 100.2.

If they mean maximum as in where the rate of change of w is 0 then that doesn't make sense either because even though the rate of change of w is 0 when x = y = z, w is at it's lowest so that would make that point into a minimum.

The only thing I can think of is that they wrote maximum instead of minimum.