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:
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.