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?
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Second partial derivative test - Wikipedia, the free encyclopedia
Originally Posted by chiph588@ Second partial derivative test - Wikipedia, the free encyclopedia which points am I testing though? I'm not sure how to write them
By substitution, Critical point: Inconclusive. Those, being , derivatives were pretty nasty though so you might want to double check them.
Last edited by dwsmith; Dec 15th 2010 at 10:36 PM. Reason: Clarification, verbage
so (0,0,0) is inconclusive but aren't there other possibilities with 1 = x^2 + y^2
No, would or satisfy
I decided to upload the image since it was interesting when I graphed.
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