- #1
manenbu
- 103
- 0
Homework Statement
Find exterma points of:
[tex]
z=1-\sqrt{x^2+y^2}[/tex]
Homework Equations
Second derivative test.
The Attempt at a Solution
I find that (0,0,1) is a point where an extremum exist. To determine whether it's a maximum or minimum I need to use the second derivative test, but my second derivatives are:
[tex]
z^{''}_{xx} = -\frac{y^2}{\sqrt{(x^2+y^2)^3}}\\
z^{''}_{yy} = -\frac{x^2}{\sqrt{(x^2+y^2)^3}}\\
z^{''}_{xy} = \frac{xy}{\sqrt{(x^2+y^2)^3}}
[/tex]
All of those functions are undefined at at x=0 and y=0.
What should I do then?
(edit - any idea why won't the "\\" make a new line in the tex code?)