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: Critical points of 2-Variable Function

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Find local max/min, and saddle points (if any) of


    This should be simple, but I am having algebra-block on solving the partial derivatives to find the critical points.

    [itex]f_x=2x+2xy=0[/itex] (1)
    [itex]f_y=2y+x^2=0[/itex] (2)

    If I multiply the second equations by -x an add it to the second and solve for x, I get

    x={0,+sqrt2, -sqrt2}

    But for some reason I cannot figure out how to solve equation 2 ?

    Why am I retarded?
  2. jcsd
  3. Oct 7, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    Well, for x=0 equation 2 gives: [itex]2y+(0)^2=0 \Rightarrow y=0[/itex] How about for x=+sqrt2?
  4. Oct 7, 2008 #3
    I guess I don't understand this.

    I want to know at what points the slope of the tangent lines is 0.

    Now, I need values of x and y that satisfy both equations simultaneously. I am used to solving the equations simultaneously, not by assigning specific values to x or y.

    I am not sure why that bothers me so much. But as you say:

    if x=0 then eq 2 is satisfied by y=0, thus (0,0) is critical

    if x=+ or - sqrt2 eq 2 is satisfied by y=-1, thus (+sqrt2, -1) and (-sqrt2, -1) are critical, yes?
  5. Oct 7, 2008 #4


    User Avatar
    Homework Helper
    Gold Member

    Yes, you can double check that those points satisfy both equations by substituting each point into them.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook