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?