Hey folks,

I'm working on this problem from the partial diff section of my book:

Verify that the sum of three numbers, x, y, and z, whose product is constant, is a minimum when they are all equal.

Just need a hint, I hope, as what I've tried, I'm not sure makes sense.

I figure I need an equation that somehow includes the constant product restriction in the sum. Maybe something like:

$\displaystyle u = x + y + z$

$\displaystyle k = xyz$

and then,

$\displaystyle u = \frac{k}{yz} + \frac{k}{xz} + \frac{k}{xy}$

Then find the total differential, and so on. I know when finding a min/max, each partial has to equal zero. But this one's getting me a little confused.

Scott