# Homework Help: Multivariable saddle point

1. Jan 2, 2012

### Doug_West

1. The problem statement, all variables and given/known data

Find and classify all relative extrema and saddle points of the function
f(x; y) = xy - x^3 - y^2.

2. Relevant equations

D = fxx *fyy -fxy^2

3. The attempt at a solution

I got D < 0 where D = -1 and fxx = 0, when x=0 and y=0. However I am unsure as to the conclusion I should arrive at when D < 0 but fxx = 0. I'm thinking that this is a saddle point?

Thanks for the help in advance,
Dough

2. Jan 2, 2012

### SammyS

Staff Emeritus
You need to find locations where both of the 1st partial derivatives are zero.

3. Jan 2, 2012

### Doug_West

yep those two pts are

x=0, y=0
and
x=1/6 y=1/12

4. Jan 2, 2012

### Doug_West

evaluating pt 0,0 I get D<0 where D= -1 and fxx(0,0) = 0, so then this is a saddle point. However is it a saddle point because D<0 or because fxx = 0?

5. Jan 2, 2012

### hangten1

guess ur doing mab127 too

when d < 0 its a saddle point doesnt matter what fxx is

6. Jan 2, 2012

### Doug_West

haha yep :D, thanks for the help.