Thread: Please check my critical points

Find the critical points of the equation
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

Originally Posted by koalamath

Find the critical points of the equation
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? 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

..

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

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 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).

I haven't checked your other answers.

ohhhh now i see it
D is less than 0 at (0,0)
I didn't see the negative
thank you so much