# Homework Help: Hessian matrix in taylor expansion help

1. Feb 6, 2012

### sdevoe

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

Find the critical point(s) of this function and determine if the function has a maxi-
mum/minimum/neither at the critical point(s) (semi colons start a new row in the matrix)

f(x,y,z) = 1/2 [ x y z ] [3 1 0; 1 4 -1; 0 -1 2] [x;y;z]

2. Relevant equations

3. The attempt at a solution
I'm fairly certain this is the second derivative of a taylor series expansion so 3rd term. So the matrix [3 1 0; 1 4 -1; 0 -1 2] is the Hessian. What I do not know now is how to get the maximum/minimum/neither or the critical points from the hessian.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 6, 2012

### sunjin09

The critical points are such that all the partial derivatives are 0

3. Feb 6, 2012

### sdevoe

So does that mean where 3x+y=0, x+4y-z=0, and -y+2z=0?

4. Feb 6, 2012

### sunjin09

yes you are right

5. Feb 6, 2012

### sdevoe

Confirming that I have to solve it as a system of equations?

6. Feb 6, 2012

### Ray Vickson

Yes, of course. That is exactly how critical points are found, in general.

RGV

7. Feb 7, 2012

### sdevoe

I will get that all the values are equal to zero if I solve that?

8. Feb 7, 2012

### Ray Vickson

Try it and see.

RGV