f(x,y) = (x^2 + y^2)e^(x^2-y^2) = z

I have found that the part ∂z/∂y = 0 when y = 0 or +/- sqrt(1 - x^2)

and that ∂z/∂x = 0 when x=0 or x^2 + y^2 + 1 = 0 which is not real

so now how do I classify them? i.e. what is min, what is max, what is saddle?

Printable View

- Dec 15th 2010, 01:43 PMPlaythiousClassifying Critical Points in R3
f(x,y) = (x^2 + y^2)e^(x^2-y^2) = z

I have found that the part ∂z/∂y = 0 when y = 0 or +/- sqrt(1 - x^2)

and that ∂z/∂x = 0 when x=0 or x^2 + y^2 + 1 = 0 which is not real

so now how do I classify them? i.e. what is min, what is max, what is saddle? - Dec 15th 2010, 02:44 PMchiph588@
- Dec 15th 2010, 09:38 PMPlaythious
- Dec 15th 2010, 10:17 PMdwsmith

By substitution,

Critical point:

Inconclusive. Those, being , derivatives were pretty nasty though so you might want to double check them. - Dec 16th 2010, 11:07 AMPlaythious
so (0,0,0) is inconclusive

but aren't there other possibilities with 1 = x^2 + y^2 - Dec 16th 2010, 02:22 PMdwsmith
No, would or satisfy

- Dec 16th 2010, 02:38 PMdwsmith
http://www.mathhelpforum.com/math-he...6&d=1292539051

I decided to upload the image since it was interesting when I graphed.