Find and classify all local maxima, minima and saddle points for the surface:

last question for my assignment

thanks!

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- Sep 4th 2008, 09:02 PMDr Zoidburgmaxima, minima, saddle point problem
Find and classify all local maxima, minima and saddle points for the surface:

last question for my assignment

thanks! - Sep 4th 2008, 09:27 PMChris L T521
Find where and

So we see that we have critical points when and

This implies that and

So we see that and

So our critical points are , , , .

Now apply the second partials test:

Recall that if:

, then has a relative minimum at

, then has a relative maximum at

, then has a saddle point at

, then no conclusion can be drawn.

Try to take it from here.

--Chris - Sep 4th 2008, 09:56 PMDr Zoidburg
thanks for that!

- Sep 5th 2008, 02:27 PMChris L T521
I checked over my work and noticed a slight error...the critical points are really . There shouldn't be any zeros in the critical points. My mistake [shouldn't be math when you're dead tired (Rofl)].

Here's the graph:

http://img.photobucket.com/albums/v4...3varmaxmin.jpg

--Chris