# Finding absolute extrema with only 1 critical point

1. Mar 12, 2013

### Reefy

1. The problem statement, all variables and given/known data
Edit: Not absolute, just extrema

I've already found the critical point to be (-1/2, -1/4, 1/2) with a value of -1/2. My only problem is finding whether this is a max or min. What technique do I use to find out? I don't believe I can use the 2nd derivative test because all the 2nd partial derivatives will equal 0.

f(x,y,z) = x + 2y + z

constraint => x^2 + 4y^2- z = 0

2. Relevant equations

3. The attempt at a solution

Critical point (-1/2, -1/4, 1/2). Value = -1/2

How do I determine whether that is a max or min?

Last edited: Mar 12, 2013
2. Mar 12, 2013

### Dick

Assuming you did everything right the best first method is just to think about it. x=0, y=0, z=0 also satisfies your contraint. So?

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