1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding absolute extrema with only 1 critical point

  1. Mar 12, 2013 #1
    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. jcsd
  3. Mar 12, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted