# Lagrange Multipliers

find min/max:

f(x,y)=xy with constraint being 4x^2+9y^2=32

## The Attempt at a Solution

I thought I understood the Lagrange problems, but I can't seem to get the minimum right on the last few problems. I get x=+/-2 and then plug back in to find y, then I use my critical points to find my min/max in f(x,y). I got 8/3 for my max on my problem (which is right), but can't get the minimum right. I set it up as such:

f(-2,-4/3)=xy and get +8/3 again, but the answer in the back of the book is -8/3 for the minimum. What am I doing wrong?

Dick
Homework Helper
You aren't doing anything wrong. But how about f(2,-4/3) or f(-2,4/3)? Nothing in the problem forces x and y to have the same sign.

You aren't doing anything wrong. But how about f(2,-4/3) or f(-2,4/3)? Nothing in the problem forces x and y to have the same sign.

- Alright, then that makes sense. The book isn't very good at pointing things out like that.

while on the topic of lagrange...When you get into having 3 variables and 1 constraint, would you set up the problem as [lambda]=x=y=z? If so, how would you solve for the unknowns?

Dick