Critical Point of Multivariable Function

[danny_manny]

Homework Statement

Locate the critical point of the function,

e^-(x^(2)+y^(2)+2x)

Homework Equations

none

The Attempt at a Solution

Ok first step differentiate the function and set it to zero for both fx and fy,

Fx(x,y) = (-2x-2)e^(-x^(2)-y^(2)-2x)
Fy = -2ye^(-x^(2)-y^(2)-2x)

Now I need to solve both equations simultaneously,

I get

ln(-2x-2)-x^(2)-y^(2)-2x = 0

and

ln(-2y)-x^(2)-y^(2)-2x = 0

and this is where I am stuck. :( any advice would be welcomed :D

thanks,
Dan

 

[Dick]

You need to solve Fx(x,y)=0. You don't want to take the log of that. log(0) is undefined, it's NOT 0. The way to do this is to notice e^a is NEVER 0. So e^(-x^(2)-y^(2)-2x) is NEVER 0. The only way Fx(x,y) could be 0 is if (2x-2) is 0.

 

[danny_manny]

ah thank you.