1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Multiple variables - check understanding

  1. Oct 27, 2007 #1
    1. The problem statement, all variables and given/known data

    A function g(x,y) = 3x^2-x-y+y^2. I have to find the minimum and maximum of the function on D = [0,1] x [0,1].

    3. The attempt at a solution

    First I have to check the ends; I mean (0,0), (0,1), (1,0) and (1,1). I also have to check the points, where the gradient is zero: (1/6,1/2).

    I insert x = 0, x = 1, y = 0 and y = 1 in g(x,y) and differentiate and equal to zero - then I have 4 new poins to check.

    I also insert x = 1/6 and y = 1/2 and do the same as above.

    So totally I have 11 points to check?
  2. jcsd
  3. Oct 27, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Hmm, I get nine points:

    1. The critical point for the open domain (0,1)*(0,1), that is (1/6,1/2)

    2. The four critical points for the function evaluated at the four boundary lines x=0, y=0, x=1 and y=1

    3. The four end points of the boundary lines, i.e, the corners (0,0), (0,1), (1,0), (1,1).
  4. Oct 27, 2007 #3
    Ok, so I do not need to insert the critical points and evaluate them (diff. and equal zero)?

    What if the gradient is something like (2x-1,1) - then only x = 0 and there's no critical points. Do I have to evaluate x = 0?

    Thank you for a quick respond!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook