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: Find stationary points of a two variable function involving

  1. Nov 24, 2015 #1
    1. The problem statement, all variables and given/known data
    Find all stationary points of the function

    G(x, y) = (x^3)*e^(−x^2−y^2)

    2. Relevant equations
    fx=0 and fy=0

    3. The attempt at a solution

    Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4)

    Gx = 0 implies 3x^2-2x^4=0


    hence x =0 ,+or- (3/2)^(1/2)

    Gy = (-2y)(x^3)(e^(-x^2-y^2))


    implies (-2y)(x^3)(e^(-x^2-y^2))=0

    y=0 x = 0

    (+or- (3/2)^(1/2), 0) are the two stationary points according to wolfram alpha but I don't understand why (o,a), where a is a real number, isn't a solution since Gx=Gy=0 when x = 0.

    Any help would be appreciated.
    Last edited by a moderator: Nov 24, 2015
  2. jcsd
  3. Nov 24, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    The points (0,a) are solutions, but (according to you---I have not checked) Wolfram Alpha seems to have missed them. Maple did not miss them.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted