1. ## Please check my critical points

Find the critical points of the equation $xy-7x^2y-9xy^2$
The critical points I found in increasing lexicographic order are
(0.0) (0,1/9),(1/21,1/27) and (1/7, 0)
at (0,0) is it undefined
at (0/1/9) and (1/7,0) you have saddle points
at (1/21,1/2) you have a local max.
Is this correct?
Thank you

2. Originally Posted by koalamath
Find the critical points of the equation $xy-7x^2y-9xy^2$
The critical points I found in increasing lexicographic order are
(0.0) (0,1/9),(1/21,1/27) and (1/7, 0)
at (0,0) is it undefined Mr F says: ?? Do you mean the test fails? ${\color{red}xy-7x^2y-9xy^2}$ is certainly not undefined at (0, 0) ....

at (0/1/9) and (1/7,0) you have saddle points
at (1/21,1/2) you have a local max.
Is this correct?
Thank you
..

3. fxx=-14y
fxx(0,0)=0
doesn't that make it undefined?

4. Originally Posted by koalamath
fxx=-14y
fxx(0,0)=0
doesn't that make it undefined?
Why? What part of the second partial derivative test says this? How can $z = xy-7x^2y-9xy^2$ be undefined when x = 0 and y = 0? z = 0, a perfectly well defined value.

In fact, there's a saddle point at (0, 0, 0).