I need to find the largest and smallest value for f(x,y) in a particular domain.

and

I found the stationary points but I have trouble when I insert the domain in f(x,y) as the answer I get is not right.

How would you solve the problem?

Thanks

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- September 19th 2009, 12:24 PMsebasto[not solved]Help finding the largest and smallest value
I need to find the largest and smallest value for f(x,y) in a particular domain.

and

I found the stationary points but I have trouble when I insert the domain in f(x,y) as the answer I get is not right.

How would you solve the problem?

Thanks - September 19th 2009, 02:07 PMSoroban
Hello, sebasto!

The domain gave me headaches, so I ignored it at the beginning.

Quote:

Find the maximum and minimum for in a given domain.

. .

. .

From [2], we have: .

If , [1] becomes: .

. . We have two critical points: .

If , [1] becomes: .

. . We have one more critical point: .

Second Partial Test: .

At . . . saddle points

At . . . extremum

. . . . . positive, concave up

Therefore: . . . . which is in the domain.

Edit: We must find the maximum(s) along the circumference of that circle.

I would use Lagrange multipliers: .

- September 19th 2009, 02:43 PMsebasto
I got the same saddle points and minimum with their respective function value, but the answer is

smallest value

Largest value

Maybe I formulated the question wrong, I'm looking for the smallest and largest value in the range - September 20th 2009, 05:25 AMsebasto
Anyone out there that has a clue on how to solve this? I have a test tomorrow and would really appreciate knowing how to solve this problem.

Thanks (Hi)