Finding absolute extrema with only 1 critical point

[Reefy]

Homework Statement

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

Homework Equations

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?

 

[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?